Journal of Commutative Algebra最新文献

{"title":"Maximal Cohen-Macaulay Complexes and Their Uses: A Partial Survey","authors":"S. Iyengar, Linquan Ma, Karl Schwede, M. Walker","doi":"10.1007/978-3-030-89694-2_15","DOIUrl":"https://doi.org/10.1007/978-3-030-89694-2_15","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89842573","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}

{"title":"Hermite Reciprocity and Schwarzenberger Bundles","authors":"Claudiu Raicu, Steven V. Sam","doi":"10.1007/978-3-030-89694-2_23","DOIUrl":"https://doi.org/10.1007/978-3-030-89694-2_23","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"74 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84411302","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}

{"title":"FT-domains and Gorenstein Prüfer v-multiplication domains","authors":"Shiqi Xing","doi":"10.1216/jca.2021.13.263","DOIUrl":"https://doi.org/10.1216/jca.2021.13.263","url":null,"abstract":"It was shown by Kang (1989) that a domain R is a Krull domain if and only if R is a Mori domain and a PvMD. In this paper, we extend this result to Gorenstein multiplicative ideal theory. To do this, we introduce the concepts of FT-domains and G-PvMDs, and study them by a new star-operation, i.e., the f-operation. We prove that (1) a domain R is an integrally closed FT-domain if and only if R is a P-domain; (2) a domain R is a G-PvMD if and only if R is a g-coherent FT-domain; (3) a domain R is a G-Krull domain if and only if R is a Mori domain and a G-Pv$v$MD.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"157 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73739476","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}

{"title":"Dedekind sums and parsing of Hilbert series","authors":"Shengtian Zhou","doi":"10.1216/jca.2021.13.281","DOIUrl":"https://doi.org/10.1216/jca.2021.13.281","url":null,"abstract":"Given a polarized variety (X,D), we can associate a graded ring and a Hilbert series. Assume D is an ample ℚ Cartier divisor, and (X,D) is quasi smooth and projectively Gorenstein, we give a parsing formula for the Hilbert series according to their singularities. Here we allow the variety to have singularities of dimension ≤1, that is, both singularities of dimension 1 and singular points, extending a 2013 result of Buckley, Reid and the author about varieties with only isolated singularities.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"304 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82878491","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}

{"title":"Syzygy bundles and the weak Lefschetz property of monomial almost complete intersections","authors":"D. Cook, U. Nagel","doi":"10.1216/jca.2021.13.157","DOIUrl":"https://doi.org/10.1216/jca.2021.13.157","url":null,"abstract":"Deciding the presence of the weak Lefschetz property often is a challenging problem. Continuing studies of Brenner and Kaid (2007), Cook II and Nagel (2011) and Migliore, Miro-Roig, Murai and Nagel (2013) we carry out an in-depth study of Artinian monomial ideals with four generators in three variables. We use a connection to lozenge tilings to describe semistability of the syzygy bundle of such an ideal, to determine its generic splitting type, and to decide the presence of the weak Lefschetz property. We provide results in both characteristic zero and positive characteristic.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"71 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84205205","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}

{"title":"Kähler Differentials for Fat Point Schemes in ℙ1×ℙ1","authors":"E. Guardo, M. Kreuzer, Tran N. K. Linh, L. N. Long","doi":"10.1216/jca.2021.13.179","DOIUrl":"https://doi.org/10.1216/jca.2021.13.179","url":null,"abstract":"Let 𝕏 be a set of K-rational points in ℙ1×ℙ1 over a field K of characteristic zero, let 𝕐 be a fat point scheme supported at 𝕏, and let R𝕐 be the bihomogeneous coordinate ring of 𝕐. In this paper we investigate the module of Kahler differentials ΩR𝕐∕K1. We describe this bigraded R𝕐-module explicitly via a homogeneous short exact sequence and compute its Hilbert function in a number of special cases, in particular when the support 𝕏 is a complete intersection or an almost complete intersection in ℙ1×ℙ1. Moreover, we introduce a Kahler different for 𝕐 and use it to characterize ACM reduced schemes in ℙ1×ℙ1 having the Cayley–Bacharach property.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"19 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72580621","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}

{"title":"Local cohomology and the multigraded regularity of ℱℐm-modules","authors":"Liping Li, Eric Ramos","doi":"10.1216/jca.2021.13.235","DOIUrl":"https://doi.org/10.1216/jca.2021.13.235","url":null,"abstract":"We develop a local cohomology theory for ℱℐm-modules, and show that it in many ways mimics the classical theory for multigraded modules over a polynomial ring. In particular, we define an invariant of ℱℐm-modules using this local cohomology theory which closely resembles an invariant of multigraded modules over Cox rings defined by Maclagan and Smith. It is then shown that this invariant behaves almost identically to the invariant of Maclagan and Smith.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"6 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90516694","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}

{"title":"Boij–Söderberg decompositions of lexicographic ideals","authors":"Sema Güntürkün","doi":"10.1216/jca.2021.13.209","DOIUrl":"https://doi.org/10.1216/jca.2021.13.209","url":null,"abstract":"Boij–Soderberg theory describes the Betti diagrams of graded modules over a polynomial ring as a linear combination of pure diagrams with positive coefficients. In this paper, we focus on the Betti diagrams of lexicographic ideals. Mainly, we characterize the Boij–Soderberg decomposition of the Betti table of a lexicographic ideal in the polynomial ring with three variables, and show a nice connection between its Boij–Soderberg decomposition and the ones of other related lexicographic ideals.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"36 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90251826","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}

{"title":"Notes on endomorphisms, local cohomology and completion","authors":"P. Schenzel","doi":"10.1090/conm/773/15540","DOIUrl":"https://doi.org/10.1090/conm/773/15540","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\">\u0000 <mml:semantics>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">M</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> denote a finitely generated module over a Noetherian ring <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\">\u0000 <mml:semantics>\u0000 <mml:mi>R</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">R</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. For an ideal <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I subset-of upper R\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>I</mml:mi>\u0000 <mml:mo>⊂<!-- ⊂ --></mml:mo>\u0000 <mml:mi>R</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">I subset R</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> there is a study of the endomorphisms of the local cohomology module <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H Subscript upper I Superscript g Baseline left-parenthesis upper M right-parenthesis comma g equals g r a d e left-parenthesis upper I comma upper M right-parenthesis comma\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msubsup>\u0000 <mml:mi>H</mml:mi>\u0000 <mml:mi>I</mml:mi>\u0000 <mml:mi>g</mml:mi>\u0000 </mml:msubsup>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>g</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mi>g</mml:mi>\u0000 <mml:mi>r</mml:mi>\u0000 <mml:mi>a</mml:mi>\u0000 <mml:mi>d</mml:mi>\u0000 <mml:mi>e</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>I</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">H^g_I(M), g = grade(I,M),</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and related results. Another subject is the study of left derived functors of the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I\">\u0000 <mml:semantics>\u0000 <mml:mi>I</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">I</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-adic completion <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Lamda Subscript i Superscript upper I Baseline left-parenthesis upper H Subscript upper I Superscript g Baseline left-parenthesis upper M right-parenthesis right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msubsup>\u0000 <mml:mi mathvariant=\"normal\">Λ<!-- Λ --></mml:mi>\u0000 <mml:mi","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"18 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80948324","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}

{"title":"Unimodular rows over monoid extensions of overrings of polynomial rings","authors":"M. A. Mathew, M. Keshari","doi":"10.1216/jca.2022.14.583","DOIUrl":"https://doi.org/10.1216/jca.2022.14.583","url":null,"abstract":"Let $R$ be a commutative Noetherian ring of dimension $d$ and $M$ a commutative cancellative torsion-free seminormal monoid. Then (1) Let $A$ be a ring of type $R[d,m,n]$ and $P$ be a projective $A[M]$-module of rank $r geq max{2,d+1}$. Then the action of $E(A[M] oplus P)$ on $Um(A[M] oplus P)$ is transitive and (2) Assume $(R, m, K)$ is a regular local ring containing a field $k$ such that either $char$ $k=0$ or $ char$ $k = p$ and $tr$-$deg$ $K/mathbb{F}_p geq 1$. Let $A$ be a ring of type $R[d,m,n]^*$ and $fin R$ be a regular parameter. Then all finitely generated projective modules over $A[M],$ $A[M]_f$ and $A[M] otimes_R R(T)$ are free. When $M$ is free both results are due to Keshari and Lokhande.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"29 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83322544","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}