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Journal of Commutative Algebra最新文献

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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":"190 1","pages":""},"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":"48 1","pages":""},"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":"19 1","pages":""},"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":"9 1","pages":""},"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":"75 1","pages":""},"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
Splitting the conormal module for licci ideals 为licci理想分割法模
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2022-03-01 DOI: 10.1216/jca.2022.14.55
Mark R. Johnson
{"title":"Splitting the conormal module for licci ideals","authors":"Mark R. Johnson","doi":"10.1216/jca.2022.14.55","DOIUrl":"https://doi.org/10.1216/jca.2022.14.55","url":null,"abstract":"For a licci ideal in a power series ring over a field, it is shown that its conormal module has a free summand precisely when the ideal is a hypersurface section. Using results of B. Ulrich, in the Gorenstein case one can show, up to deformation, that the conormal module is indecomposable.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"21 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75113873","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
Well-covered and Cohen–Macaulay theta-ring graphs 完备覆盖图和Cohen-Macaulay环图
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2021-12-01 DOI: 10.1216/jca.2021.13.461
Iván D. Castrillón, E. Reyes
{"title":"Well-covered and Cohen–Macaulay theta-ring graphs","authors":"Iván D. Castrillón, E. Reyes","doi":"10.1216/jca.2021.13.461","DOIUrl":"https://doi.org/10.1216/jca.2021.13.461","url":null,"abstract":"In this paper we characterize the wellcovered property for: theta-ring and ring graphs. Furthermore, we prove that Cohen-Macaulayness, pure shellability and pure vertex decomposability are equivalent for theta-ring graphs. Also, we give a combinatorial characterization of these graphs.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"18 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73298844","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 some classes of integral domains with finitely many star operations of finite type 一类有限多有限型星型运算的积分域
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2021-12-01 DOI: 10.1216/jca.2021.13.489
Abdulilah Kadri, A. Mimouni
{"title":"On some classes of integral domains with finitely many star operations of finite type","authors":"Abdulilah Kadri, A. Mimouni","doi":"10.1216/jca.2021.13.489","DOIUrl":"https://doi.org/10.1216/jca.2021.13.489","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"27 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81450789","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 implicit constant fields and key polynomials for valuation algebraic extensions 关于估值代数扩展的隐式常数域和关键多项式
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2021-11-29 DOI: 10.1216/jca.2022.14.515
Arpan Dutta
{"title":"On the implicit constant fields and key polynomials for valuation algebraic extensions","authors":"Arpan Dutta","doi":"10.1216/jca.2022.14.515","DOIUrl":"https://doi.org/10.1216/jca.2022.14.515","url":null,"abstract":"This article is a natural continuation of our previous works [7] and [6]. In this article, we employ similar ideas as in [4] to provide an estimate of IC(K(X)|K, v) when (K(X)|K, v) is a valuation algebraic extension. Our central result is an analogue of [6, Theorem 1.3]. We further provide a natural construction of a complete sequence of key polynomials for v over K in the setting of valuation algebraic extensions.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"219 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75131837","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
Cohen–Macaulay property and linearity of pinched Veronese rings 紧缩型Veronese环的Cohen-Macaulay性质和线性
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2021-11-01 DOI: 10.1216/jca.2021.13.347
Ornella Greco, Ivan Martino
{"title":"Cohen–Macaulay property and linearity of pinched Veronese rings","authors":"Ornella Greco, Ivan Martino","doi":"10.1216/jca.2021.13.347","DOIUrl":"https://doi.org/10.1216/jca.2021.13.347","url":null,"abstract":"In this work, we study the Betti numbers of pinched Veronese rings, by means of the reduced homology of squarefree divisor complexes. We characterize when these rings are Cohen-Macaulay and we study the shape of the Betti tables for the pinched Veronese in the two variables. As a byproduct we obtain information on the linearity of such rings. Moreover, in the last section we compute the canonical modules of the Veronese modules. The Veronese embedding injects the projective space Pn−1 into PN−1 by sending x = [x1 : x2 : · · · : xn] to the point with projective coordinates all possible monomials x1 1 . . . x in n of degree d, so N = ( n+d−1 d ) . The d-Veronese ring, S, is the coordinate ring of the image of the d-th Veronese embedding of Pn−1, with S = K[x1, . . . , xn]. The pinched Veronese map is another embedding of Pn−1, but this time the target space is PN−2 and the components of the image of x are all but one of the possible monomials. We denote such monomial by x. The coordinate ring of the latter image of Pn−1 is called pinched Veronese rings, Pn,d,m. The koszul property of the pinched Veronese rings was a trendy topic in literature. Peeva and Sturmfels asked whether the pinched Veronese ring P3,3,(1,1,1) is Koszul. A positive answer was given by Caviglia in [7], and then reproved by Caviglia and Conca in [8], and, after, in [9]; later, Tancer [21] generalized this result to Pn,n,(1,...,1). Vu used a combinatorial approach to prove that Pn,d,m is Koszul, unless d ≥ 3 and m is one of the permutations of (d− 2, 2, 0, . . . , 0), see [22]. 1991 AMS Mathematics subject classification. 13D02; 13D40; 05E99; 13C14, 13A02.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"26 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90908579","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
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