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Quasi-F-splittings in birational geometry III 双向几何中的准 F 分裂 III
arXiv - MATH - Commutative Algebra Pub Date : 2024-08-04 DOI: arxiv-2408.01921
Tatsuro Kawakami, Teppei Takamatsu, Hiromu Tanaka, Jakub Witaszek, Fuetaro Yobuko, Shou Yoshikawa
{"title":"Quasi-F-splittings in birational geometry III","authors":"Tatsuro Kawakami, Teppei Takamatsu, Hiromu Tanaka, Jakub Witaszek, Fuetaro Yobuko, Shou Yoshikawa","doi":"arxiv-2408.01921","DOIUrl":"https://doi.org/arxiv-2408.01921","url":null,"abstract":"We prove that $mathbb Q$-Gorenstein quasi-$F$-regular singularities are klt.\u0000To this end, we shall introduce quasi-test ideals.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Blowup algebras of ladder or interval determinantal modules 阶梯或区间行列式模块的吹胀代数
arXiv - MATH - Commutative Algebra Pub Date : 2024-08-04 DOI: arxiv-2408.01903
Kuei-Nuan Lin, Yi-Huang Shen
{"title":"Blowup algebras of ladder or interval determinantal modules","authors":"Kuei-Nuan Lin, Yi-Huang Shen","doi":"arxiv-2408.01903","DOIUrl":"https://doi.org/arxiv-2408.01903","url":null,"abstract":"We determine Gr\"{o}bner bases for the presentation ideals of multi-Rees\u0000algebras and their special fiber rings. Specifically, we focus on modules that\u0000are direct sums of ideals generated by either maximal minors of a two-sided\u0000ladder matrix or unit interval determinantal ideals. Our analysis reveals that\u0000the multi-blowup algebras are Koszul Cohen--Macaulay normal domains, possess\u0000rational singularities in characteristic zero, and are F-rational in positive\u0000characteristic.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On weakly S-primary hyyperideals 关于弱 S 主次全等
arXiv - MATH - Commutative Algebra Pub Date : 2024-08-03 DOI: arxiv-2408.01758
Mahdi Anbarloei
{"title":"On weakly S-primary hyyperideals","authors":"Mahdi Anbarloei","doi":"arxiv-2408.01758","DOIUrl":"https://doi.org/arxiv-2408.01758","url":null,"abstract":"In this paper, our purpose is to introduce and study the notion of weakly\u0000n-ary S-primary hyperideals in a commutative Krasner (m,n)-hyperring.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multiplicative Lattices with Absorbing Factorization 带吸收因式分解的乘法网格
arXiv - MATH - Commutative Algebra Pub Date : 2024-08-02 DOI: arxiv-2408.01100
Andreas Reinhart, Gulsen Ulucak
{"title":"Multiplicative Lattices with Absorbing Factorization","authors":"Andreas Reinhart, Gulsen Ulucak","doi":"arxiv-2408.01100","DOIUrl":"https://doi.org/arxiv-2408.01100","url":null,"abstract":"In [22], Yassine et al. introduced the notion of 1-absorbing prime ideals in\u0000commutative rings with nonzero identity. In this article, we examine the\u0000concept of 1-absorbing prime elements in C-lattices. We investigate the\u0000C-lattices in which every element is a finite product of 1-absorbing prime\u0000elements (we denote them as OAFLs for short). Moreover, we study C-lattices\u0000having 2-absorbing factorization (we denote them as TAFLs for short).","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the two-dimensional Jacobian conjecture: Magnus' formula revisited, IV 关于二维雅各布猜想：马格努斯公式再探，IV
arXiv - MATH - Commutative Algebra Pub Date : 2024-08-02 DOI: arxiv-2408.01279
Kyungyong Lee, Li Li
{"title":"On the two-dimensional Jacobian conjecture: Magnus' formula revisited, IV","authors":"Kyungyong Lee, Li Li","doi":"arxiv-2408.01279","DOIUrl":"https://doi.org/arxiv-2408.01279","url":null,"abstract":"Let $(F,G)$ be a Jacobian pair with $d=wtext{-deg}(F)$ and\u0000$e=wtext{-deg}(G)$ for some direction $w$. A generalized Magnus' formula\u0000approximates $G$ as $sum_{gammage 0} c_gamma F^{frac{e-gamma}{d}}$ for\u0000some complex numbers $c_gamma$. We develop an approach to the two-dimensional\u0000Jacobian conjecture, aiming to minimize the use of terms corresponding to\u0000$gamma>0$. As an initial step in this approach, we define and study the inner\u0000polynomials of $F$ and $G$. The main result of this paper shows that the\u0000northeastern vertex of the Newton polygon of each inner polynomial is located\u0000within a specific region. As applications of this result, we introduce several\u0000conjectures and prove some of them for special cases.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weakly S-prime hyperideals 弱 S 素超等数
arXiv - MATH - Commutative Algebra Pub Date : 2024-08-01 DOI: arxiv-2408.00430
Mahdi Anbarloei
{"title":"Weakly S-prime hyperideals","authors":"Mahdi Anbarloei","doi":"arxiv-2408.00430","DOIUrl":"https://doi.org/arxiv-2408.00430","url":null,"abstract":"In this paper, we aim to introduce weakly $n$-ary $S$-prime hyperideals in a\u0000commutative Krasner $(m,n)$-hyperring.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A ring of cohomological operators on Ext and Tor Ext 和 Tor 上的同调算子环
arXiv - MATH - Commutative Algebra Pub Date : 2024-08-01 DOI: arxiv-2408.00730
Samuel Alvite, Javier Majadas
{"title":"A ring of cohomological operators on Ext and Tor","authors":"Samuel Alvite, Javier Majadas","doi":"arxiv-2408.00730","DOIUrl":"https://doi.org/arxiv-2408.00730","url":null,"abstract":"For any homomorphism of commutative rings $A to B$ and a $B$-module $M$, we\u0000construct a structure of graded $mathrm{S}_B^{ast}mathrm{H}^1(A,B,B)$-module\u0000on $mathrm{Ext}_B^{ast}(M,M)$ and $mathrm{Tor}_{ast}^B(M,M)$, where\u0000$mathrm{H}^1(A,B,B)$ is the first Andr'e-Quillen cohomology module and\u0000$mathrm{S}^{ast}$ denotes the symmetric algebra. This structure generalizes\u0000the well known structures of $B[X_1, dots, X_n]$-module constructed by\u0000Gulliksen when $B=R/I$ and $I$ is generated by a regular sequence of length $n$\u0000(in this case, $mathrm{S}_B^{ast}mathrm{H}^1(R,B,B)= mathrm{S}_B^{ast}\u0000left(widehat{I/I^2}right)=B[X_1, dots, X_n]$), but the main interest is\u0000that for any such $B=R/I$, Gulliksen operations factorize through the ring\u0000$mathrm{S}_B^{ast}mathrm{H}^1(A,B,B)$ for any ring $A$ such that $R$ is an\u0000$A$-algebra, allowing us to think that, for some purposes, in order to define\u0000these cohomological operations, Andr'e-Quillen cohomology is a more natural\u0000choice than the normal module $widehat{I/I^2}$.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Prime ideals of Moh and the characteristic of the field 墨的质心和域的特征
arXiv - MATH - Commutative Algebra Pub Date : 2024-07-31 DOI: arxiv-2407.21692
Laura González, Francesc Planas-Vilanova
{"title":"Prime ideals of Moh and the characteristic of the field","authors":"Laura González, Francesc Planas-Vilanova","doi":"arxiv-2407.21692","DOIUrl":"https://doi.org/arxiv-2407.21692","url":null,"abstract":"We reprove and generalize a result of Moh which bounds the minimal number of\u0000generators of an ideal in a power series ring in three variables over a field.\u0000As a consequence, we obtain minimal generating sets for the first prime of Moh,\u0000proving that the minimal number of generators might decrease depending on the\u0000field characteristic. This contradicts an statement of Sally. Finally, we show\u0000that these minimal generating sets are standard basis with the negative degree\u0000reverse lexicographic order.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The poset of normalized ideals of numerical semigroups with multiplicity three 乘数为三的数字半群归一化理想的正集
arXiv - MATH - Commutative Algebra Pub Date : 2024-07-31 DOI: arxiv-2407.21697
S. Bonzio, P. A. García-Sánchez
{"title":"The poset of normalized ideals of numerical semigroups with multiplicity three","authors":"S. Bonzio, P. A. García-Sánchez","doi":"arxiv-2407.21697","DOIUrl":"https://doi.org/arxiv-2407.21697","url":null,"abstract":"We study the poset of normalized ideals of a numerical semigroup with\u0000multiplicity three. We show that this poset is always a lattice, and that two\u0000different numerical semigroups with multiplicity three have non-isomorphic\u0000posets of normalized ideals.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An explicit upper bound for the HSL number of the top local cohomology module of affine semigroup rings 仿射半群环顶局部同调模块 HSL 数的明确上限
arXiv - MATH - Commutative Algebra Pub Date : 2024-07-31 DOI: arxiv-2407.21731
Havi Ellers
{"title":"An explicit upper bound for the HSL number of the top local cohomology module of affine semigroup rings","authors":"Havi Ellers","doi":"arxiv-2407.21731","DOIUrl":"https://doi.org/arxiv-2407.21731","url":null,"abstract":"The Hartshorne-Speiser-Lyubeznik number is a numerical invariant that can\u0000often be used to bound the Frobenius test exponent of positive characteristic\u0000rings. In this paper we look at positive characteristic semigroup rings\u0000generated by affine torsion-free abelian cancellative pointed semigroups that\u0000contain an identity, and compute an upper bound for the\u0000Hartshorne-Speiser-Lyubeznik number of their top local cohomology module at the\u0000maximal monomial ideal.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"213 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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