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Journal of Commutative Algebra最新文献

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A COLORFUL HOCHSTER FORMULA AND UNIVERSAL PARAMETERS FOR FACE RINGS 一个丰富多彩的hochster公式和通用参数的面环
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2020-07-25 DOI: 10.1216/jca.2023.15.151
Ashleigh Adams, V. Reiner
{"title":"A COLORFUL HOCHSTER FORMULA AND UNIVERSAL PARAMETERS FOR FACE RINGS","authors":"Ashleigh Adams, V. Reiner","doi":"10.1216/jca.2023.15.151","DOIUrl":"https://doi.org/10.1216/jca.2023.15.151","url":null,"abstract":"This paper has two related parts. The first generalizes Hochster's formula on resolutions of Stanley-Reisner rings to a colorful version, applicable to any proper vertex-coloring of a simplicial complex. The second part examines a universal system of parameters for Stanley-Reisner rings of simplicial complexes, and more generally, face rings of simplicial posets. These parameters have good properties, including being fixed under symmetries, and detecting depth of the face ring. Moreover, when resolving the face ring over these parameters, the shape is predicted, conjecturally, by the colorful Hochster formula.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"46 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87907566","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
Stickelberger and the Eigenvalue Theorem 斯蒂克尔伯格和特征值定理
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2020-07-24 DOI: 10.1007/978-3-030-89694-2_8
David A. Cox
{"title":"Stickelberger and the Eigenvalue Theorem","authors":"David A. Cox","doi":"10.1007/978-3-030-89694-2_8","DOIUrl":"https://doi.org/10.1007/978-3-030-89694-2_8","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"16 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89582931","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: 11
Stillman’s question for twisted commutative algebras 扭曲交换代数的Stillman问题
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2020-07-06 DOI: 10.1216/jca.2022.14.315
Karthik Ganapathy
{"title":"Stillman’s question for twisted commutative algebras","authors":"Karthik Ganapathy","doi":"10.1216/jca.2022.14.315","DOIUrl":"https://doi.org/10.1216/jca.2022.14.315","url":null,"abstract":"Let $mathbf{A}_{n, m}$ be the polynomial ring $text{Sym}(mathbf{C}^n otimes mathbf{C}^m)$ with the natural action of $mathbf{GL}_m(mathbf{C})$. We construct a family of $mathbf{GL}_m(mathbf{C})$-stable ideals $J_{n, m}$ in $mathbf{A}_{n, m}$, each equivariantly generated by one homogeneous polynomial of degree $2$. Using the Ananyan-Hochster principle, we show that the regularity of this family is unbounded. This negatively answers a question raised by Erman-Sam-Snowden on a generalization of Stillman's conjecture.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"15 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74021233","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
Examples of multiplicities and mixed multiplicities of filtrations 多重和混合多重过滤的例子
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2020-07-05 DOI: 10.1090/conm/773/15530
S. Cutkosky
{"title":"Examples of multiplicities and mixed multiplicities of filtrations","authors":"S. Cutkosky","doi":"10.1090/conm/773/15530","DOIUrl":"https://doi.org/10.1090/conm/773/15530","url":null,"abstract":"In this paper we construct examples of irrational behavior of multiplicities and mixed multiplicities of divisorial filtrations. The construction makes essential use of anti-positive intersection products.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83050404","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: 7
A locally F-finite Noetherian domain that is not F-finite 不是f有限的局部f有限诺瑟域
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2020-06-10 DOI: 10.1216/jca.2022.14.177
T. Dumitrescu, Cristodor Ionescu
{"title":"A locally F-finite Noetherian domain that is not F-finite","authors":"T. Dumitrescu, Cristodor Ionescu","doi":"10.1216/jca.2022.14.177","DOIUrl":"https://doi.org/10.1216/jca.2022.14.177","url":null,"abstract":"Using an old example of Nagata, we construct a Noetherian ring of prime characteristic p, whose Frobenius morphism is locally finite, but not finite.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"47 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72480406","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
ON THE UBIQUITY OF ARF RINGS 关于无处不在的艺术戒指
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2020-06-02 DOI: 10.1216/jca.2023.15.177
Ela Celikbas, Olgur Celikbas, Cuatualin Ciupercua, Naoki Endo, S. Goto, Ryotaro Isobe, Naoyuki Matsuoka
{"title":"ON THE UBIQUITY OF ARF RINGS","authors":"Ela Celikbas, Olgur Celikbas, Cuatualin Ciupercua, Naoki Endo, S. Goto, Ryotaro Isobe, Naoyuki Matsuoka","doi":"10.1216/jca.2023.15.177","DOIUrl":"https://doi.org/10.1216/jca.2023.15.177","url":null,"abstract":"We introduce and develop the theory of weakly Arf rings, which is a generalization of Arf rings, initially defined by J. Lipman in 1971. We provide characterizations of weakly Arf rings and study the relation between these rings, the Arf rings, and the strict closedness of rings. Furthermore, we give various examples of weakly Arf rings that come from idealizations, fiber products, determinantal rings, and invariant subrings.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"110 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85776266","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: 3
Quaternion rational surfaces 四元数有理曲面
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2020-06-01 DOI: 10.1216/jca.2020.12.237
J. W. Hoffman, Xiaohong Jia, Haohao Wang
{"title":"Quaternion rational surfaces","authors":"J. W. Hoffman, Xiaohong Jia, Haohao Wang","doi":"10.1216/jca.2020.12.237","DOIUrl":"https://doi.org/10.1216/jca.2020.12.237","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"50 1","pages":"237-261"},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89230534","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 finitely stable domains, II 在有限稳定定义域上
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2020-06-01 DOI: 10.1216/jca.2020.12.179
Stefania Gabelli, M. Roitman
{"title":"On finitely stable domains, II","authors":"Stefania Gabelli, M. Roitman","doi":"10.1216/jca.2020.12.179","DOIUrl":"https://doi.org/10.1216/jca.2020.12.179","url":null,"abstract":"Among other results, we prove the following: (1) A locally Archimedean stable domain satisfies accp. (2) A stable domain R is Archimedean if and only if every nonunit of R belongs to a height-one prime ideal of R′ (this result is related to Ohm’s Theorem for Prüfer domains). (3) An Archimedean stable domain R is one-dimensional if and only if R′ is equidimensional (generally, an Archimedean stable local domain is not necessarily onedimensional). (4) An Archimedean finitely stable semilocal domain with stable maximal ideals is locally Archimedean, but generally, neither Archimedean stable domains, nor Archimedean semilocal domains are necessarily locally Archimedean.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"33 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76215636","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: 3
Witt–Burnside functor attached to $boldsymbol{Z}_{p}^{2}$ and $p$-adic Lipschitz continuous functions 附于$boldsymbol{Z}_{p}^{2}$和$p$-adic Lipschitz连续函数的Witt-Burnside函子
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2020-06-01 DOI: 10.1216/jca.2020.12.263
L. Miller, B. Steinhurst
{"title":"Witt–Burnside functor attached to $boldsymbol{Z}_{p}^{2}$ and $p$-adic Lipschitz continuous functions","authors":"L. Miller, B. Steinhurst","doi":"10.1216/jca.2020.12.263","DOIUrl":"https://doi.org/10.1216/jca.2020.12.263","url":null,"abstract":"Dress and Siebeneicher gave a significant generalization of the construction of Witt vectors, by producing for any profinite group G , a ring-valued functor W G . This paper gives the first concrete interpretation of any Witt–Burnside rings outside the procyclic cases in terms of known rings. In particular, the rings W Z p 2 ( k ) , where k is a field of characteristic p > 0 have a quotient realized as rings of Lipschitz continuous functions on the p -adic upper half plane P 1 ( Q p ) . As a consequence we show that the Krull dimensions of the rings W Z p d ( k ) are infinite for d ≥ 2 and we show the Teichmuller representatives form an analogue of the van der Put basis for continuous functions on Z p .","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"47 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79012419","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
Weak normality and seminormality in the mixed characteristic case 混合特征情况下的弱正态和半正态
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2020-04-24 DOI: 10.1216/jca.2022.14.351
Jun Horiuchi, Kazuma Shimomoto
{"title":"Weak normality and seminormality in the mixed characteristic case","authors":"Jun Horiuchi, Kazuma Shimomoto","doi":"10.1216/jca.2022.14.351","DOIUrl":"https://doi.org/10.1216/jca.2022.14.351","url":null,"abstract":"In this article, we give a few examples of local rings in relation to weak normality and seminormality in mixed characteristic. It is known that two concepts can differ in the equal prime characteristic case, while they coincide in the equal characteristic zero case. No explicit examples seem to be documented in the existing literature in the mixed characteristic case. We also establish the local Bertini theorem for weak normality in mixed characteristic under a certain condition.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76576349","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
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