Journal of Commutative Algebra最新文献

{"title":"The Alexander–Hirschowitz Theorem and Related Problems","authors":"Huy Tài Hà, P. Mantero","doi":"10.1007/978-3-030-89694-2_12","DOIUrl":"https://doi.org/10.1007/978-3-030-89694-2_12","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72584862","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":"AUSLANDER’S THEOREM AND N-ISOLATED SINGULARITIES","authors":"Josh Stangle","doi":"10.1216/jca.2023.15.115","DOIUrl":"https://doi.org/10.1216/jca.2023.15.115","url":null,"abstract":"One of the most stunning results in the representation theory of Cohen-Macaulay rings is Auslander's well known theorem which states a CM local ring of finite CM type can have at most an isolated singularity. There have been some generalizations of this in the direction of countable CM type by Huneke and Leuschke. In this paper, we focus on a different generalization by restricting the class of modules. Here we consider modules which are high syzygies of MCM modules over non-commutative rings, exploiting the fact that non-commutative rings allow for finer homological behavior. We then generalize Auslander's Theorem in the setting of complete Gorenstein local domains by examining path algebras, which preserve finiteness of global dimension.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91010741","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":"On finite molecularization domains","authors":"Andrew J. Hetzel, Anna L. Lawson, Andreas Reinhart","doi":"10.1216/JCA.2021.13.69","DOIUrl":"https://doi.org/10.1216/JCA.2021.13.69","url":null,"abstract":"In this paper, we advance an ideal-theoretic analogue of a \"finite factorization domain\" (FFD), giving such a domain the moniker \"finite molecularization domain\" (FMD). We characterize FMD's as those factorable domains (termed \"molecular domains\" in the paper) for which every nonzero ideal is divisible by only finitely many nonfactorable ideals (termed \"molecules\" in the paper) and the monoid of nonzero ideals of the domain is unit-cancellative, in the language of Fan, Geroldinger, Kainrath, and Tringali. We develop a number of connections, particularly at the local level, amongst the concepts of \"FMD\", \"FFD\", and the \"finite superideal domains\" (FSD's) of Hetzel and Lawson. Characterizations of when $k[X^2, X^3]$, where $k$ is a field, and the classical $D+M$ construction are FMD's are provided. We also demonstrate that if $R$ is a Dedekind domain with the finite norm property, then $R[X]$ is an FMD.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87496426","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":"Which Properties of Stanley–Reisner Rings and Simplicial Complexes are Topological?","authors":"V. Welker","doi":"10.1007/978-3-030-89694-2_27","DOIUrl":"https://doi.org/10.1007/978-3-030-89694-2_27","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76466170","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":"Existence and Constructions of Totally Reflexive Modules","authors":"Adela Vraciu","doi":"10.1007/978-3-030-89694-2_25","DOIUrl":"https://doi.org/10.1007/978-3-030-89694-2_25","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72801270","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":"A generalization of coefficient ideals","authors":"P. Lima","doi":"10.1090/conm/773/15537","DOIUrl":"https://doi.org/10.1090/conm/773/15537","url":null,"abstract":"<p>In this paper we give a generalization of the coefficient ideals of an <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"German m\"> <mml:semantics> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"fraktur\">m</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathfrak {m}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-primary ideal <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I\"> <mml:semantics> <mml:mi>I</mml:mi> <mml:annotation encoding=\"application/x-tex\">I</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in a quasi-unmixed local ring <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=\"application/x-tex\">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with infinite residue field.</p>","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78850280","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":"Applications of Liaison","authors":"J. Migliore, U. Nagel","doi":"10.1007/978-3-030-89694-2_17","DOIUrl":"https://doi.org/10.1007/978-3-030-89694-2_17","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75600910","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":"The Étale locus in complete local rings","authors":"R. Heitmann","doi":"10.1090/conm/773/15532","DOIUrl":"https://doi.org/10.1090/conm/773/15532","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=\"application/x-tex\">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a complete local ring and let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Q\"> <mml:semantics> <mml:mi>Q</mml:mi> <mml:annotation encoding=\"application/x-tex\">Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a prime ideal of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=\"application/x-tex\">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. It is determined precisely which conditions on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=\"application/x-tex\">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are equivalent to the existence of a complete unramified regular local ring <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A\"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=\"application/x-tex\">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and an element <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g element-of upper A minus upper Q\"> <mml:semantics> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mi>A</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mi>Q</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">gin A-Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=\"application/x-tex\">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a finite <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A\"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=\"application/x-tex\">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-module and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A Subscript g Baseline long right-arrow upper R Subscript g\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">⟶<!-- ⟶ --></mml:mo> ","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79735692","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":"Tate resolutions and MCM approximations","authors":"D. Eisenbud, F. Schreyer","doi":"10.1090/conm/773/15531","DOIUrl":"https://doi.org/10.1090/conm/773/15531","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding=\"application/x-tex\">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a finitely generated Cohen-Macaulay module of codimension <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"m\"> <mml:semantics> <mml:mi>m</mml:mi> <mml:annotation encoding=\"application/x-tex\">m</mml:annotation> </mml:semantics> </mml:math> </inline-formula> over a Gorenstein Ring <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R equals upper S slash upper I\"> <mml:semantics> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo>=</mml:mo> <mml:mi>S</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>I</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">R = S/I</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S\"> <mml:semantics> <mml:mi>S</mml:mi> <mml:annotation encoding=\"application/x-tex\">S</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a regular ring. We show how to form a quasi-isomorphism <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"phi\"> <mml:semantics> <mml:mi>ϕ<!-- ϕ --></mml:mi> <mml:annotation encoding=\"application/x-tex\">phi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> from an <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=\"application/x-tex\">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-free resolution of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding=\"application/x-tex\">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to the dual of an <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=\"application/x-tex\">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-free resolution of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M Superscript logical-or Baseline colon-equal normal upper E normal x normal t Subscript upper R Superscript m Baseline left-parenthesis upper M comma upper R right-parenthesis\"> <mml:semantics> <mml:mr","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89262554","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":"Magic squares of squares over a finite field","authors":"S. Hengeveld, Giancarlo Labruna, Aihua Li","doi":"10.1090/conm/773/15536","DOIUrl":"https://doi.org/10.1090/conm/773/15536","url":null,"abstract":"<p>A magic square <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding=\"application/x-tex\">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> over an integral domain <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D\"> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding=\"application/x-tex\">D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3 times 3\"> <mml:semantics> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>×<!-- × --></mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">3times 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> matrix with entries from <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D\"> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding=\"application/x-tex\">D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that the elements from each row, column, and diagonal add to the same sum. If all the entries in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding=\"application/x-tex\">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are perfect squares in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D\"> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding=\"application/x-tex\">D</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we call <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding=\"application/x-tex\">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a magic square of squares over <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D\"> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding=\"application/x-tex\">D</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In 1984, Martin LaBar raised an open question: “Is there a magic square of squares over the ring <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Z\"> <mml:semantics> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">Z</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathbb {Z}</mml:annotation> ","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85803885","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}