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Journal of Commutative Algebra最新文献

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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":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":"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
Elasticities of Krull monoids with infinite cyclic class group 具有无限循环类群的Krull模群的弹性
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2021-11-01 DOI: 10.1216/jca.2021.13.449
X. Zeng, Guixin Deng
{"title":"Elasticities of Krull monoids with infinite cyclic class group","authors":"X. Zeng, Guixin Deng","doi":"10.1216/jca.2021.13.449","DOIUrl":"https://doi.org/10.1216/jca.2021.13.449","url":null,"abstract":"Let H be a Krull monoid with infinite cyclic class group G that we identify with Z. Let GP ⊆ G denote the set of classes containing prime divisors. It was shown that ρ(H), the elasticity of H, is finite if and only if GP is bounded above or below. By a result of Lambert, it is easy to show that ρ(H) ≤ min{− inf(GP ), sup(GP )}. In this paper, we focus on H with large elasticity. When GP is infinite but bounded above or below, we give necessary and sufficient conditions for that ρ(H) > min{− inf(GP ), sup(GP )} − 3/2. When GP is a finite set, we give a better upper bound on ρ(H), which is sharp in some sense.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84219892","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
Lower Bounds on Betti Numbers 关于贝蒂数的下界
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2021-08-12 DOI: 10.1007/978-3-030-89694-2_2
Adam Boocher, Eloísa Grifo
{"title":"Lower Bounds on Betti Numbers","authors":"Adam Boocher, Eloísa Grifo","doi":"10.1007/978-3-030-89694-2_2","DOIUrl":"https://doi.org/10.1007/978-3-030-89694-2_2","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82314110","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
Castelnuovo–Mumford Regularity and Powers 卡斯特尔诺沃-芒福德规则与权力
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2021-07-30 DOI: 10.1007/978-3-030-89694-2_4
W. Bruns, A. Conca, M. Varbaro
{"title":"Castelnuovo–Mumford Regularity and Powers","authors":"W. Bruns, A. Conca, M. Varbaro","doi":"10.1007/978-3-030-89694-2_4","DOIUrl":"https://doi.org/10.1007/978-3-030-89694-2_4","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84044406","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: 5
Fibers of Rational Maps and Elimination Matrices: An Application Oriented Approach 有理映射和消去矩阵的纤维:面向应用的方法
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2021-07-29 DOI: 10.1007/978-3-030-89694-2_6
Laurent Bus'e, M. Chardin
{"title":"Fibers of Rational Maps and Elimination Matrices: An Application Oriented Approach","authors":"Laurent Bus'e, M. Chardin","doi":"10.1007/978-3-030-89694-2_6","DOIUrl":"https://doi.org/10.1007/978-3-030-89694-2_6","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80307886","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
Three Takes on Almost Complete Intersection Ideals of Grade 3 三取三年级几乎完全相交理想
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2021-06-28 DOI: 10.1007/978-3-030-89694-2_7
Lars Christensen, Oana Veliche, J. Weyman
{"title":"Three Takes on Almost Complete Intersection Ideals of Grade 3","authors":"Lars Christensen, Oana Veliche, J. Weyman","doi":"10.1007/978-3-030-89694-2_7","DOIUrl":"https://doi.org/10.1007/978-3-030-89694-2_7","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88370279","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
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