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{"title":"New sequence spaces derived by using generalized arithmetic divisor sum function and compact operators","authors":"Taja Yaying, Nipen Saikia, Mohammad Mursaleen","doi":"10.1515/forum-2023-0138","DOIUrl":"https://doi.org/10.1515/forum-2023-0138","url":null,"abstract":"Define an infinite matrix <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msup> <m:mi mathvariant=\"fraktur\">D</m:mi> <m:mi>α</m:mi> </m:msup> <m:mo>=</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:msubsup> <m:mi>d</m:mi> <m:mrow> <m:mi>n</m:mi> <m:mo>,</m:mo> <m:mi>v</m:mi> </m:mrow> <m:mi>α</m:mi> </m:msubsup> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0138_ineq_0001.png\" /> <jats:tex-math>mathfrak{D}^{alpha}=(d^{alpha}_{n,v})</jats:tex-math> </jats:alternatives> </jats:inline-formula> by <jats:disp-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msubsup> <m:mi>d</m:mi> <m:mrow> <m:mi>n</m:mi> <m:mo>,</m:mo> <m:mi>v</m:mi> </m:mrow> <m:mi>α</m:mi> </m:msubsup> <m:mo>=</m:mo> <m:mrow> <m:mo>{</m:mo> <m:mtable columnspacing=\"5pt\" displaystyle=\"true\" rowspacing=\"0pt\"> <m:mtr> <m:mtd columnalign=\"left\"> <m:mrow> <m:mfrac> <m:msup> <m:mi>v</m:mi> <m:mi>α</m:mi> </m:msup> <m:mrow> <m:msup> <m:mi>σ</m:mi> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>α</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>n</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:mfrac> <m:mo>,</m:mo> </m:mrow> </m:mtd> <m:mtd columnalign=\"left\"> <m:mrow> <m:mrow> <m:mi>v</m:mi> <m:mo>∣</m:mo> <m:mi>n</m:mi> </m:mrow> <m:mo>,</m:mo> </m:mrow> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign=\"left\"> <m:mrow> <m:mn>0</m:mn> <m:mo>,</m:mo> </m:mrow> </m:mtd> <m:mtd columnalign=\"left\"> <m:mrow> <m:mrow> <m:mi>v</m:mi> <m:mo>∤</m:mo> <m:mi>n</m:mi> </m:mrow> <m:mo>,</m:mo> </m:mrow> </m:mtd> </m:mtr> </m:mtable> </m:mrow> </m:mrow> </m:math> <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0138_eq_9999.png\" /> <jats:tex-math>d^{alpha}_{n,v}=begin{cases}dfrac{v^{alpha}}{sigma^{(alpha)}(n)},&vmid n, 0,&vnmid n,end{cases}</jats:tex-math> </jats:alternatives> </jats:disp-formula> where <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msup> <m:mi>σ</m:mi> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>α</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>n</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0138_ineq_0002.png\" /> <jats:tex-math>sigma^{(alpha)}(n)</jats:tex-math> </jats:alternatives> </jats:inline-formula> is defined to be the sum of the 𝛼-th power of the positive divisors of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>n</m:mi> <m:mo>∈</m:mo> <m:mi mathvariant=\"double-struck\">N</m:mi> </m:mrow> </m:math> <jats:inline-gr","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140035232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Building planar polygon spaces from the projective braid arrangement","authors":"Navnath Daundkar, Priyavrat Deshpande","doi":"10.1515/forum-2023-0032","DOIUrl":"https://doi.org/10.1515/forum-2023-0032","url":null,"abstract":"The moduli space of planar polygons with generic side lengths is a smooth, closed manifold. It is known that these manifolds contain the moduli space of distinct points on the real projective line as an open dense subset. Kapranov showed that the real points of the Deligne–Mumford–Knudson compactification can be obtained from the projective Coxeter complex of type 𝐴 (equivalently, the projective braid arrangement) by iteratively blowing up along the minimal building set. In this paper, we show that these planar polygon spaces can also be obtained from the projective Coxeter complex of type 𝐴 by performing an iterative cellular surgery along a subcollection of the minimal building set. Interestingly, this subcollection is determined by the combinatorial data associated with the length vector called the genetic code.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"59 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140002472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Joint distribution of the cokernels of random p-adic matrices II","authors":"Jiwan Jung, Jungin Lee","doi":"10.1515/forum-2023-0131","DOIUrl":"https://doi.org/10.1515/forum-2023-0131","url":null,"abstract":"In this paper, we study the combinatorial relations between the cokernels <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>cok</m:mi> <m:mo>⁡</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:msub> <m:mi>A</m:mi> <m:mi>n</m:mi> </m:msub> <m:mo>+</m:mo> <m:mrow> <m:mi>p</m:mi> <m:mo>⁢</m:mo> <m:msub> <m:mi>x</m:mi> <m:mi>i</m:mi> </m:msub> <m:mo>⁢</m:mo> <m:msub> <m:mi>I</m:mi> <m:mi>n</m:mi> </m:msub> </m:mrow> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0131_eq_0646.png\" /> <jats:tex-math>{operatorname{cok}(A_{n}+px_{i}I_{n})}</jats:tex-math> </jats:alternatives> </jats:inline-formula> (<jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mn>1</m:mn> <m:mo>≤</m:mo> <m:mi>i</m:mi> <m:mo>≤</m:mo> <m:mi>m</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0131_eq_0323.png\" /> <jats:tex-math>{1leq ileq m}</jats:tex-math> </jats:alternatives> </jats:inline-formula>), where <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>A</m:mi> <m:mi>n</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0131_eq_0378.png\" /> <jats:tex-math>{A_{n}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is an <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>n</m:mi> <m:mo>×</m:mo> <m:mi>n</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0131_eq_0825.png\" /> <jats:tex-math>{ntimes n}</jats:tex-math> </jats:alternatives> </jats:inline-formula> matrix over the ring of <jats:italic>p</jats:italic>-adic integers <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>ℤ</m:mi> <m:mi>p</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0131_eq_0584.png\" /> <jats:tex-math>{mathbb{Z}_{p}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>I</m:mi> <m:mi>n</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0131_eq_0431.png\" /> <jats:tex-math>{I_{n}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>n</m:mi> <m:mo>×</m:mo> <m:mi>n</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"30 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some properties of extended frame measure","authors":"Jinjun Li, Zhiyi Wu, Fusheng Xiao","doi":"10.1515/forum-2023-0412","DOIUrl":"https://doi.org/10.1515/forum-2023-0412","url":null,"abstract":"We prove that the extended frame spectral measures are of pure type and the Beurling dimension of any frame measure for an extended frame spectral measure is in its Fourier dimension and upper entropy dimension.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"76 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Orthogonal separation of variables for spaces of constant curvature","authors":"Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev","doi":"10.1515/forum-2023-0300","DOIUrl":"https://doi.org/10.1515/forum-2023-0300","url":null,"abstract":"We construct all orthogonal separating coordinates in constant curvature spaces of arbitrary signature. Further, we construct explicit transformation between orthogonal separating and flat or generalised flat coordinates, as well as explicit formulas for the corresponding Killing tensors and Stäckel matrices.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"51 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uniform bounds for Kloosterman sums of half-integral weight with applications","authors":"Qihang Sun","doi":"10.1515/forum-2023-0201","DOIUrl":"https://doi.org/10.1515/forum-2023-0201","url":null,"abstract":"Sums of Kloosterman sums have deep connections with the theory of modular forms, and their estimation has many important consequences. Kuznetsov used his famous trace formula and got a power-saving estimate with respect to <jats:italic>x</jats:italic> with implied constants depending on <jats:italic>m</jats:italic> and <jats:italic>n</jats:italic>. Recently, in 2009, Sarnak and Tsimerman obtained a bound uniformly in <jats:italic>x</jats:italic>, <jats:italic>m</jats:italic> and <jats:italic>n</jats:italic>. The generalized Kloosterman sums are defined with multiplier systems and on congruence subgroups. Goldfeld and Sarnak bounded sums of them with main terms corresponding to exceptional eigenvalues of the hyperbolic Laplacian. Their error term is a power of <jats:italic>x</jats:italic> with implied constants depending on all the other factors. In this paper, for a wide class of half-integral weight multiplier systems, we get the same bound with the error term uniformly in <jats:italic>x</jats:italic>, <jats:italic>m</jats:italic> and <jats:italic>n</jats:italic>. Such uniform bounds have great applications. For the eta-multiplier, Ahlgren and Andersen obtained a uniform and power-saving bound with respect to <jats:italic>m</jats:italic> and <jats:italic>n</jats:italic>, which resulted in a convergent error estimate on the Rademacher exact formula of the partition function <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>p</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>n</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0201_eq_0934.png\" /> <jats:tex-math>{p(n)}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. We also establish a Rademacher-type exact formula for the difference of partitions of rank modulo 3, which allows us to apply our power-saving estimate to the tail of the formula for a convergent error bound.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"238 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"q-supercongruences from Watson's 8φ7 transformation","authors":"Xiaoxia Wang, Chang Xu","doi":"10.1515/forum-2023-0409","DOIUrl":"https://doi.org/10.1515/forum-2023-0409","url":null,"abstract":"Employing Watson’s <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mmultiscripts> <m:mi>ϕ</m:mi> <m:mn>7</m:mn> <m:none /> <m:mprescripts /> <m:mn>8</m:mn> <m:none /> </m:mmultiscripts> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0409_eq_0156.png\" /> <jats:tex-math>{{}_{8}phi_{7}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> transformation formula, we unearth several <jats:italic>q</jats:italic>-supercongruences with a parameter <jats:italic>s</jats:italic>. Particularly, one of our results is an extension of a <jats:italic>q</jats:italic>-analogue of Van Hamme’s (G.2) supercongruence. In addition, we obtain a <jats:italic>q</jats:italic>-supercongruence modulo the fifth power of a cyclotomic polynomial and propose two related conjectures.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"13 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fundamental properties of Cauchy–Szegő projection on quaternionic Siegel upper half space and applications","authors":"Der-Chen Chang, Xuan Thinh Duong, Ji Li, Wei Wang, Qingyan Wu","doi":"10.1515/forum-2024-0049","DOIUrl":"https://doi.org/10.1515/forum-2024-0049","url":null,"abstract":"We investigate the Cauchy–Szegő projection for quaternionic Siegel upper half space to obtain the pointwise (higher order) regularity estimates for Cauchy–Szegő kernel and prove that the Cauchy–Szegő kernel is nonzero everywhere, which further yields a non-degenerated pointwise lower bound. As applications, we prove the uniform boundedness of Cauchy–Szegő projection on every atom on the quaternionic Heisenberg group, which is used to give an atomic decomposition of regular Hardy space <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>H</m:mi> <m:mi>p</m:mi> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2024-0049_eq_0488.png\" /> <jats:tex-math>{H^{p}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> on quaternionic Siegel upper half space for <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mfrac> <m:mn>2</m:mn> <m:mn>3</m:mn> </m:mfrac> <m:mo>&lt;</m:mo> <m:mi>p</m:mi> <m:mo>≤</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2024-0049_eq_0631.png\" /> <jats:tex-math>{frac{2}{3}&lt;pleq 1}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Moreover, we establish the characterisation of singular values of the commutator of Cauchy–Szegő projection based on the kernel estimates. The quaternionic structure (lack of commutativity) is encoded in the symmetry groups of regular functions and the associated partial differential equations.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"34 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Submodules of normalisers in groupoid C*-algebras and discrete group coactions","authors":"Fuyuta Komura","doi":"10.1515/forum-2023-0182","DOIUrl":"https://doi.org/10.1515/forum-2023-0182","url":null,"abstract":"In this paper, we investigate certain submodules in C*-algebras associated to effective étale groupoids. First, we show that a submodule generated by normalizers is a closure of the set of compactly supported continuous functions on some open set. As a corollary, we show that discrete group coactions on groupoid C*-algebras are induced by cocycles of étale groupoids if the fixed point algebras contain C*-subalgebras of continuous functions vanishing at infinity on the unit spaces. In the latter part, we prove the Galois correspondence result for discrete group coactions on groupoid C*-algebras.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"190 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cellular covers of divisible uniserial modules over valuation domains","authors":"László Fuchs, Brendan Goldsmith, Luigi Salce, Lutz Strüngmann","doi":"10.1515/forum-2023-0351","DOIUrl":"https://doi.org/10.1515/forum-2023-0351","url":null,"abstract":"Cellular covers which originate in homotopy theory are considered here for a very special class: divisible uniserial modules over valuation domains. This is a continuation of the study of cellular covers of divisible objects, but in order to obtain more substantial results, we are restricting our attention further to specific covers or to specific kernels. In particular, for <jats:italic>h</jats:italic>-divisible uniserial modules, we deal first with covers limited to divisible torsion-free modules (Section 3), and continue with the restriction to torsion standard uniserials (Sections 4–5). For divisible non-standard uniserial modules, only those cellular covers are investigated whose kernels are also divisible non-standard uniserials (Section 6). The results are specific enough to enable us to describe more accurately how to find all cellular covers obeying the chosen restrictions.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"6 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139656233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}