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Journal of Commutative Algebra最新文献

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GENERATING POLYNOMIALS FOR THE DISTRIBUTION OF GENERALIZED BINOMIAL COEFFICIENTS IN DISCRETE VALUATION DOMAINS 离散估值域中广义二项式系数分布的多项式生成
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2023-03-01 DOI: 10.1216/jca.2023.15.65
Dong Quan Ngoc Nguyen
{"title":"GENERATING POLYNOMIALS FOR THE DISTRIBUTION OF GENERALIZED BINOMIAL COEFFICIENTS IN DISCRETE VALUATION DOMAINS","authors":"Dong Quan Ngoc Nguyen","doi":"10.1216/jca.2023.15.65","DOIUrl":"https://doi.org/10.1216/jca.2023.15.65","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76909324","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 power series with a limited number of factorizations 有限次分解的广义幂级数
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2022-12-01 DOI: 10.1216/jca.2022.14.471
Ngoc P. Aylesworth, J. R. Juett
{"title":"Generalized power series with a limited number of factorizations","authors":"Ngoc P. Aylesworth, J. R. Juett","doi":"10.1216/jca.2022.14.471","DOIUrl":"https://doi.org/10.1216/jca.2022.14.471","url":null,"abstract":". Several past authors have studied questions related to unique factorization of generalized power series. Here we examine the broader topic of generalized power series that (in a sense we will make precise) have a limited number of factorizations. Special cases of our general results include new results about “limited factorization” in (Laurent) power series rings, (Laurent) polynomial rings, and the “large polynomial rings” of Halter-Koch. Along the way to our main results, we study Krull domains and Cohen-Kaplansky rings of generalized power series and give several slight extensions to the fundamental ring theory of generalized power series.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87238206","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 lattices over one-dimensional noetherian domains 一维诺瑟域上的广义格
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2022-11-01 DOI: 10.1216/jca.2022.14.443
P. Př́ıhoda
{"title":"Generalized lattices over one-dimensional noetherian domains","authors":"P. Př́ıhoda","doi":"10.1216/jca.2022.14.443","DOIUrl":"https://doi.org/10.1216/jca.2022.14.443","url":null,"abstract":"We study direct sum decompositions of pure projective torsion free modules over one-dimensional commutative noetherian domains. Having an inspiration in the representation theory of orders in separable algebras we study when every pure projective torsion free module is a direct sum of finitely generated modules. A satisfactory criterion is given for analytically unramified reduced local rings and for Bass domains.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81896862","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
Countably totally projective Abelian p-groups have minimal full inertia 可数全射影阿贝尔p群具有极小的满惯性
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2022-11-01 DOI: 10.1216/jca.2022.14.427
P. Keef
{"title":"Countably totally projective Abelian p-groups have minimal full inertia","authors":"P. Keef","doi":"10.1216/jca.2022.14.427","DOIUrl":"https://doi.org/10.1216/jca.2022.14.427","url":null,"abstract":"A new class of abelian p-groups is introduced, the countably totally projective groups, that contains the well-known class of totally projective groups. A countably totally projective group is shown to have the property that every fully inert subgroup is commensurable with a fully invariant subgroup. This generalizes results of Goldsmith, Salce and Zanardo (2014), who proved that a direct sum of cyclic p-groups has this property. It also answers affirmatively two questions recently posed in the literature.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72815220","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
Resolutions of ideals of subspace arrangements 子空间排列理想的分解
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2022-11-01 DOI: 10.1216/jca.2022.14.319
Francesca Gandini
{"title":"Resolutions of ideals of subspace arrangements","authors":"Francesca Gandini","doi":"10.1216/jca.2022.14.319","DOIUrl":"https://doi.org/10.1216/jca.2022.14.319","url":null,"abstract":"Given a collection of t subspaces in an ndimensional vector space W we can associate to them t linear ideals in the symmetric algebra S(W ∗). Conca and Herzog showed that the Castelnuovo-Mumford regularity of the product of t linear ideals is equal to t. Derksen and Sidman showed that the Castelnuovo-Mumford regularity of the intersection of t linear ideals is at most t. In this paper we show that analogous results hold when we work over the exterior algebra ∧ (W ∗) (over a field of characteristic 0). To prove these results we rely on the functoriality of equivariant free resolutions and construct a functor Ω from the category of polynomial functors to itself. The functor Ω transforms resolutions of polynomial functors associated to subspace arrangements over the symmetric algebra to resolutions over the exterior algebra.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75482004","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
Interpolation over ℤ and torsion in class groups 类群上的插值与扭转
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2022-11-01 DOI: 10.1216/jca.2022.14.309
John D. Berman, D. Erman
{"title":"Interpolation over ℤ and torsion in class groups","authors":"John D. Berman, D. Erman","doi":"10.1216/jca.2022.14.309","DOIUrl":"https://doi.org/10.1216/jca.2022.14.309","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86823081","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
MAC LANE–VAQUIÉ CHAINS AND VALUATION-TRANSCENDENTAL EXTENSIONS Mac lane-vaquiÉ链和超值扩展
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2022-09-24 DOI: 10.1216/jca.2023.15.249
Sneha Mavi, Anuj Bishnoi
{"title":"MAC LANE–VAQUIÉ CHAINS AND VALUATION-TRANSCENDENTAL EXTENSIONS","authors":"Sneha Mavi, Anuj Bishnoi","doi":"10.1216/jca.2023.15.249","DOIUrl":"https://doi.org/10.1216/jca.2023.15.249","url":null,"abstract":"In this paper, for a valued field $(K, v)$ of arbitrary rank and an extension $w$ of $v$ to $K(X),$ we give a connection between complete sets of ABKPs for $w$ and MacLane-Vaqui'e chains of $w.$","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87944685","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
On the nonrigidity of trace modules 论跟踪模块的非刚性
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2022-06-01 DOI: 10.1216/jca.2022.14.277
H. Lindo
{"title":"On the nonrigidity of trace modules","authors":"H. Lindo","doi":"10.1216/jca.2022.14.277","DOIUrl":"https://doi.org/10.1216/jca.2022.14.277","url":null,"abstract":"We establish a link between trace modules and rigidity in modules over Noetherian rings. We identify classes of modules which must have self-extensions and use the theory of trace ideals to verify the Auslander-Reiten conjecture for syzygies of ideals over Artinian Gorenstein rings.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74893224","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
On regularity bounds and linear resolutions of toric algebras of graphs 图的环代数的正则界和线性分辨
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2022-06-01 DOI: 10.1216/jca.2022.14.285
Rimpa Nandi, Ramakrishna Nanduri
{"title":"On regularity bounds and linear resolutions of toric algebras of graphs","authors":"Rimpa Nandi, Ramakrishna Nanduri","doi":"10.1216/jca.2022.14.285","DOIUrl":"https://doi.org/10.1216/jca.2022.14.285","url":null,"abstract":"Let G be a simple graph. In this article we show that if G is connected and R(I(G)) is normal, then reg(R(I(G))) ≤ α0(G), where α0(G) the vertex cover number of G. As a consequence, every normal König connected graph G, reg(R(I(G))) = mat(G), the matching number of G. For a gap-free graph G, we give various combinatorial upper bounds for reg(R(I(G))). As a consequence we give various sufficient conditions for the equality of reg(R(I(G))) and mat(G). Finally we show that if G is a chordal graph such that K[G] has q-linear resolution (q ≥ 4), then K[G] is a hypersurface, which proves the conjecture of Hibi-Matsuda-Tsuchiya [12, Conjecture 0.2], affirmatively for chordal graphs.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90961580","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
Module-theoretic characterizations of the ring of finite fractions of a commutative ring 交换环有限分数环的模论刻画
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2022-03-01 DOI: 10.1216/jca.2022.14.141
Fangping Wang, D. Zhou, Dan Chen
{"title":"Module-theoretic characterizations of the ring of finite fractions of a commutative ring","authors":"Fangping Wang, D. Zhou, Dan Chen","doi":"10.1216/jca.2022.14.141","DOIUrl":"https://doi.org/10.1216/jca.2022.14.141","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86086199","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: 14
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