Journal of Pure and Applied Algebra最新文献_第5页

Projective surfaces not as Hadamard products and the dimensions of the Hadamard joins

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107853

Edoardo Ballico

引用次数: 0

Non-finitely generated monoids corresponding to finitely generated homogeneous subalgebras

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107854

Akihiro Higashitani, Koichiro Tani

{"title":"Non-finitely generated monoids corresponding to finitely generated homogeneous subalgebras","authors":"Akihiro Higashitani, Koichiro Tani","doi":"10.1016/j.jpaa.2024.107854","DOIUrl":"10.1016/j.jpaa.2024.107854","url":null,"abstract":"<div><div>The goal of this paper is to study the possible monoids appearing as the associated monoids of the initial algebra of a finitely generated homogeneous <span><math><mi>k</mi></math></span>-subalgebra of a polynomial ring <span><math><mi>k</mi><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math></span>. Clearly, any affine monoid can be realized since the initial algebra of the affine monoid <span><math><mi>k</mi></math></span>-algebra is itself. On the other hand, the initial algebra of a finitely generated homogeneous <span><math><mi>k</mi></math></span>-algebra is not necessarily finitely generated. In this paper, we provide a new family of non-finitely generated monoids which can be realized as the initial algebras of finitely generated homogeneous <span><math><mi>k</mi></math></span>-algebras. Moreover, we also provide an example of a non-finitely generated monoid which cannot be realized as the initial algebra of any finitely generated homogeneous <span><math><mi>k</mi></math></span>-algebra.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107854"},"PeriodicalIF":0.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143094023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Frobenius and quasi-Frobenius left Hopf algebroids

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107844

Sophie Chemla

引用次数: 0

Colimits in 2-dimensional slices

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107855

Luca Mesiti

{"title":"Colimits in 2-dimensional slices","authors":"Luca Mesiti","doi":"10.1016/j.jpaa.2024.107855","DOIUrl":"10.1016/j.jpaa.2024.107855","url":null,"abstract":"<div><div>We generalize to dimension 2 the well-known fact that a colimit in a 1-dimensional slice is precisely the map from the colimit of the domains of the diagram that is induced by the universal property. For this, we find the need to reduce weighted 2-colimits to cartesian-marked oplax conical ones, and as a consequence the need to consider lax slices.</div><div>We prove results of preservation, reflection and lifting of 2-colimits for the domain 2-functor from a lax slice. We thus generalize to dimension 2 the whole fruitful calculus of colimits in 1-dimensional slices. We achieve this within the framework of enhanced (or <span><math><mi>F</mi></math></span>-)category theory. The preservation result assumes products in the base 2-category and uses an original general theorem which states that a lax left adjoint preserves appropriate 2-colimits if the adjunction is strict on one side and suitably <span><math><mi>F</mi></math></span>-categorical.</div><div>Finally, we apply the same general theorem of preservation of 2-colimits to the 2-functor of change of base along a split Grothendieck opfibration between lax slices. We prove that this change of base 2-functor is indeed a left adjoint of the kind described above by laxifying the proof that Conduché functors are exponentiable. We conclude extending the result of preservation of 2-colimits for the change of base 2-functor to any finitely complete 2-category with a dense generator.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107855"},"PeriodicalIF":0.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143099039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Determining the Betti numbers of R/(xpe,ype,zpe) for most even degree hypersurfaces in odd characteristic

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107858

Heath Camphire

{"title":"Determining the Betti numbers of R/(xpe,ype,zpe) for most even degree hypersurfaces in odd characteristic","authors":"Heath Camphire","doi":"10.1016/j.jpaa.2024.107858","DOIUrl":"10.1016/j.jpaa.2024.107858","url":null,"abstract":"<div><div>Let <em>k</em> be a field of odd characteristic <em>p</em>. Fix an even number <span><math><mi>d</mi><mo><</mo><mi>p</mi><mo>+</mo><mn>1</mn></math></span> and a power <span><math><mi>q</mi><mo>≥</mo><mi>d</mi><mo>+</mo><mn>3</mn></math></span> of <em>p</em>. For most choices of degree <em>d</em> standard graded hypersurfaces <span><math><mi>R</mi><mo>=</mo><mi>k</mi><mo>[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>]</mo><mo>/</mo><mo>(</mo><mi>f</mi><mo>)</mo></math></span> with homogeneous maximal ideal <span><math><mi>m</mi></math></span>, we can determine the graded Betti numbers of <span><math><mi>R</mi><mo>/</mo><msup><mrow><mi>m</mi></mrow><mrow><mo>[</mo><mi>q</mi><mo>]</mo></mrow></msup></math></span>. In fact, given two fixed powers <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≥</mo><mi>d</mi><mo>+</mo><mn>3</mn></math></span>, for most choices of <em>R</em> the graded Betti numbers in high homological degree of <span><math><mi>R</mi><mo>/</mo><msup><mrow><mi>m</mi></mrow><mrow><mo>[</mo><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>]</mo></mrow></msup></math></span> and <span><math><mi>R</mi><mo>/</mo><msup><mrow><mi>m</mi></mrow><mrow><mo>[</mo><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>]</mo></mrow></msup></math></span> are the same up to a constant shift. This paper shows this fact by combining our results with the work of Miller, Rahmati, and R.G. on link-<em>q</em>-compressed polynomials in <span><span>[13]</span></span>. We show that link-<em>q</em>-compressed polynomials are indeed fairly common in many polynomial rings.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107858"},"PeriodicalIF":0.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143099041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Automorphisms of quartic surfaces and Cremona transformations

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107850

Daniela Paiva , Ana Quedo

引用次数: 0

Free automorphism groups of K3 surfaces with Picard number 3

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107845

Kenji Hashimoto , Kwangwoo Lee

引用次数: 0

Minimal and cellular free resolutions over polynomial OI-algebras

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107856

Nathan Fieldsteel , Uwe Nagel

{"title":"Minimal and cellular free resolutions over polynomial OI-algebras","authors":"Nathan Fieldsteel , Uwe Nagel","doi":"10.1016/j.jpaa.2024.107856","DOIUrl":"10.1016/j.jpaa.2024.107856","url":null,"abstract":"<div><div>Minimal free resolutions of graded modules over a noetherian polynomial ring have been attractive objects of interest for more than a hundred years. We introduce and study two natural extensions in the setting of graded modules over a polynomial OI-algebra, namely <em>minimal</em> and <em>width-wise minimal</em> free resolutions. A minimal free resolution of an OI-module can be characterized by the fact that the free module in every fixed homological degree, say <em>i</em>, has minimal rank among all free resolutions of the module. We show that any finitely generated graded module over a noetherian polynomial OI-algebra admits a graded minimal free resolution and that it is unique. A width-wise minimal free resolution is a free resolution that provides a minimal free resolution of a module in every width. Such a resolution is necessarily minimal. Its existence is not guaranteed. However, we show that certain monomial OI-ideals do admit width-wise minimal free or, more generally, width-wise minimal flat resolutions. These ideals include families of well-known monomial ideals such as Ferrers ideals and squarefree strongly stable ideals. The arguments rely on the theory of cellular resolutions.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107856"},"PeriodicalIF":0.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143094024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Prime group graded rings with applications to partial crossed products and Leavitt path algebras

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107842

Daniel Lännström , Patrik Lundström , Johan Öinert , Stefan Wagner

引用次数: 0

An inductive model structure for strict ∞-categories

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107859

Simon Henry , Félix Loubaton

{"title":"An inductive model structure for strict ∞-categories","authors":"Simon Henry , Félix Loubaton","doi":"10.1016/j.jpaa.2024.107859","DOIUrl":"10.1016/j.jpaa.2024.107859","url":null,"abstract":"<div><div>We construct a left semi-model category of “marked strict ∞-categories” for which the fibrant objects are those whose marked arrows satisfy natural closure properties and are invertible up to higher marked arrows. The canonical model structure on strict ∞-categories can be recovered as a left Bousfield localization of this model structure. We show that an appropriate extension of the Street nerve to the marked setting produces a Quillen adjunction between our model category and the Verity model structure for complicial sets, generalizing previous results by the second named author. Finally, we use this model structure to study, in the setting of strict ∞-categories, the idea that, because they are two different “truncation functors” taking an <span><math><mo>(</mo><mo>∞</mo><mo>,</mo><mi>n</mi><mo>)</mo></math></span> to an <span><math><mo>(</mo><mo>∞</mo><mo>,</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-category, there are two non-equivalent definitions for the <span><math><mo>(</mo><mo>∞</mo><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-category of <span><math><mo>(</mo><mo>∞</mo><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>-categories as a limit of the <span><math><mo>(</mo><mo>∞</mo><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-categories of <span><math><mo>(</mo><mo>∞</mo><mo>,</mo><mi>n</mi><mo>)</mo></math></span>-categories. We show that in fact there seem to be at least three non-equivalent ways of constructing an <span><math><mo>(</mo><mo>∞</mo><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-category of <span><math><mo>(</mo><mo>∞</mo><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>-categories.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107859"},"PeriodicalIF":0.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143099040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0