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Linear resolutions and quasi-linearity of monomial ideals 单项理想的线性分辨率和拟线性
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2022-02-21 DOI: 10.7146/math.scand.a-136634
D. Lu
{"title":"Linear resolutions and quasi-linearity of monomial ideals","authors":"D. Lu","doi":"10.7146/math.scand.a-136634","DOIUrl":"https://doi.org/10.7146/math.scand.a-136634","url":null,"abstract":"We introduce the notion of quasi-linearity and prove it is necessary for a monomial ideal to have a linear resolution and clarify all the quasi-linear monomial ideals generated in degree $2$. We also introduce the notion of a strongly linear monomial over a monomial ideal and prove that if $mathbf {u}$ is a monomial strongly linear over $I$ then $I$ has a linear resolution (respectively is quasi-linear) if and only if $I+mathbf {u}mathfrak {p}$ has a linear resolution (respectively is quasi-linear). Here $mathfrak {p}$ is any monomial prime ideal.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49566635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Complexity and rigidity of Ulrich modules, and some applications Ulrich模的复杂性和刚性及其应用
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2022-01-04 DOI: 10.7146/math.scand.a-136499
Souvik Dey, D. Ghosh
{"title":"Complexity and rigidity of Ulrich modules, and some applications","authors":"Souvik Dey, D. Ghosh","doi":"10.7146/math.scand.a-136499","DOIUrl":"https://doi.org/10.7146/math.scand.a-136499","url":null,"abstract":"We analyze whether Ulrich modules, not necessarily maximal CM (Cohen-Macaulay), can be used as test modules, which detect finite homological dimensions of modules. We prove that Ulrich modules over CM local rings have maximal complexity and curvature. Various new characterizations of local rings are provided in terms of Ulrich modules. We show that every Ulrich module of dimension $s$ over a local ring is $(s+1)$-Tor-rigid-test, but not $s$−Tor-rigid in general (where $sge 1$). Over a deformation of a CM local ring of minimal multiplicity, we also study Tor rigidity.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45588373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Topological boundaries of covariant representations 协变表示的拓扑边界
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-12-17 DOI: 10.7146/math.scand.a-135771
M. Amini, Sajad Zavar
{"title":"Topological boundaries of covariant representations","authors":"M. Amini, Sajad Zavar","doi":"10.7146/math.scand.a-135771","DOIUrl":"https://doi.org/10.7146/math.scand.a-135771","url":null,"abstract":"We associate a boundary $mathcal B_{pi ,u}$ to each covariant representation $(pi ,u,H)$ of a $C^*$-dynamical system $(G,A,alpha )$ and study the action of $G$ on $mathcal B_{pi ,u}$ and its amenability properties. We relate rigidity properties of traces on the associated crossed product $C^*$-algebra to faithfulness of the action of the group on this boundary.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46206336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lifts, transfers, and degrees of univariate maps 单变量映射的提升、转移和阶数
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-12-08 DOI: 10.7146/math.scand.a-134457
T. Brazelton, Stephen McKean
{"title":"Lifts, transfers, and degrees of univariate maps","authors":"T. Brazelton, Stephen McKean","doi":"10.7146/math.scand.a-134457","DOIUrl":"https://doi.org/10.7146/math.scand.a-134457","url":null,"abstract":"One can compute the local $mathbb{A}^1$-degree at points with separable residue field by base changing, working rationally, and post-composing with the field trace. We show that for endomorphisms of the affine line, one can compute the local $mathbb{A}^1$-degree at points with inseparable residue field by taking a suitable lift of the polynomial and transferring its local degree. We also discuss the general set-up and strategy in terms of the six functor formalism. As an application, we show that trace forms of number fields are local $mathbb{A}^1$-degrees.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47098113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Results on the normality of square-free monomial ideals and cover ideals under some graph operations 关于一些图运算下无平方单理想和覆盖理想的正规性的结果
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-11-30 DOI: 10.7146/math.scand.a-128963
Ibrahim Al-Ayyoub, M. Nasernejad, K. Khashyarmanesh, L. Roberts, V. C. Quiñonez
{"title":"Results on the normality of square-free monomial ideals and cover ideals under some graph operations","authors":"Ibrahim Al-Ayyoub, M. Nasernejad, K. Khashyarmanesh, L. Roberts, V. C. Quiñonez","doi":"10.7146/math.scand.a-128963","DOIUrl":"https://doi.org/10.7146/math.scand.a-128963","url":null,"abstract":"In this paper, we introduce techniques for producing normal square-free monomial ideals from old such ideals. These techniques are then used to investigate the normality of cover ideals under some graph operations. Square-free monomial ideals that come out as linear combinations of two normal ideals are shown to be not necessarily normal; under such a case we investigate the integral closedness of all powers of these ideals.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42951480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Singular integrals and sublinear operators on amalgam spaces and Hardy-amalgam spaces 汞齐空间和Hardy汞齐空间上的奇异积分和次线性算子
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-11-30 DOI: 10.7146/math.scand.a-128966
K. Ho
{"title":"Singular integrals and sublinear operators on amalgam spaces and Hardy-amalgam spaces","authors":"K. Ho","doi":"10.7146/math.scand.a-128966","DOIUrl":"https://doi.org/10.7146/math.scand.a-128966","url":null,"abstract":"In this paper, we establish the extrapolation theory for the amalgam spaces and the Hardy-amalgam spaces. By using the extrapolation theory, we obtain the mapping properties for the Calderón-Zygmund operators and its commutator, the Carleson operators and establish the Rubio de Francia inequalities for Littlewood-Paley functions of arbitrary intervals to the amalgam spaces. We also obtain the boundedness of the Calder{ó}n-Zygmund operators and the intrinsic square function on the Hardy-amalgam spaces.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44453123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Product property of global $P$-extremal functions 全局$P$极值函数的乘积性质
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-11-30 DOI: 10.7146/math.scand.a-129007
N. Q. Dieu, T. V. Long
{"title":"Product property of global $P$-extremal functions","authors":"N. Q. Dieu, T. V. Long","doi":"10.7146/math.scand.a-129007","DOIUrl":"https://doi.org/10.7146/math.scand.a-129007","url":null,"abstract":"In this note, we establish a product property for $P$-extremal functions in the same spirit as the original product formula due to J. Siciak in Ann. Polon. Math., 39 (1981), 175–211. As a consequence, we obtain convexity for the sublevel sets of such extremal functions. Moreover, we also generalize the product property of $P$-extremal functions established by L. Bos and N. Levenberg in Comput. Methods Funct. Theory 18 (2018), 361–388, and later by N. Levenberg and M. Perera, in Contemporary Mathematics 743 (2020), 11–19, in which no restriction on $P$ is needed.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45902559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On homotopy nilpotency of the octonian plane $mathbb{O}P^2$ 关于八阶平面$mathbb的同态幂零性{O}P^2$
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-11-30 DOI: 10.7146/math.scand.a-128541
Marek Golasi´nski
{"title":"On homotopy nilpotency of the octonian plane $mathbb{O}P^2$","authors":"Marek Golasi´nski","doi":"10.7146/math.scand.a-128541","DOIUrl":"https://doi.org/10.7146/math.scand.a-128541","url":null,"abstract":"Let $mathbb{O}P^2_{(p)}$ be the $p$-localization of the Cayley projective plane $mathbb{O}P^2$ for a prime $p$ or $p=0$. We show that the homotopy nilpotency class $textrm{nil} Omega(mathbb{O}P^2_{(p)})<infty $ for $p>2$ and $textrm{nil} Omega (mathbb{O}P^2_{(p)})=1$ for $p>5$ or $p=0$. The homotopy nilpotency of remaining Rosenfeld projective planes are discussed as well.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46531093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized John Gromov hyperbolic domains and extensions of maps 广义John Gromov双曲域与映射的扩展
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-11-30 DOI: 10.7146/math.scand.a-128968
Qingshan Zhou, Liulan Li, A. Rasila
{"title":"Generalized John Gromov hyperbolic domains and extensions of maps","authors":"Qingshan Zhou, Liulan Li, A. Rasila","doi":"10.7146/math.scand.a-128968","DOIUrl":"https://doi.org/10.7146/math.scand.a-128968","url":null,"abstract":"Let $Omega subset mathbb{R}^n$ be a Gromov hyperbolic, $varphi$-length John domain. We show that there is a uniformly continuous identification between the inner boundary of $Omega$ and the Gromov boundary endowed with a visual metric, By using this result, we prove the boundary continuity not only for quasiconformal homeomorphisms, but also for more generally rough quasi-isometries between the domains equipped with the quasihyperbolic metrics.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47722906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Non-Lebesgue measurability of finite unions of Vitali selectors related to different groups 与不同群体相关的Vitali选择器有限联合的非勒贝格可测性
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-11-30 DOI: 10.7146/math.scand.a-128969
Venuste Nyagahakwa, Gratien Haguma
{"title":"Non-Lebesgue measurability of finite unions of Vitali selectors related to different groups","authors":"Venuste Nyagahakwa, Gratien Haguma","doi":"10.7146/math.scand.a-128969","DOIUrl":"https://doi.org/10.7146/math.scand.a-128969","url":null,"abstract":"In this paper, we prove that each topological group isomorphism of the additive topological group $(mathbb{R},+)$ of real numbers onto itself preserves the non-Lebesgue measurability of Vitali selectors of $mathbb{R}$. Inspired by Kharazishvili's results, we further prove that each finite union of Vitali selectors related to different countable dense subgroups of $(mathbb{R}, +)$, is not measurable in the Lebesgue sense. From here, we produce a semigroup of sets, for which elements are not measurable in the Lebesgue sense. We finally show that the produced semigroup is invariant under the action of the group of all affine transformations of $mathbb{R}$ onto itself.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41960400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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