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RINGS WITH AN ELEMENTARY ABELIAN p-GROUP OF UNITS 带有基本阿贝尔 p 单位组的戒指
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2023-12-01 DOI: 10.1216/jca.2023.15.469
Sunil K. Chebolu, J. Corry, Elizabeth Grimm, Andrew Hatfield
{"title":"RINGS WITH AN ELEMENTARY ABELIAN p-GROUP OF UNITS","authors":"Sunil K. Chebolu, J. Corry, Elizabeth Grimm, Andrew Hatfield","doi":"10.1216/jca.2023.15.469","DOIUrl":"https://doi.org/10.1216/jca.2023.15.469","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138986457","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 ABELIAN GROUPS HAVING ISOMORPHIC PROPER CHARACTERISTIC SUBGROUPS 在具有同构适当特征子群的非良性群上
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2023-12-01 DOI: 10.1216/jca.2023.15.481
A. Chekhlov, P. Danchev
{"title":"ON ABELIAN GROUPS HAVING ISOMORPHIC PROPER CHARACTERISTIC SUBGROUPS","authors":"A. Chekhlov, P. Danchev","doi":"10.1216/jca.2023.15.481","DOIUrl":"https://doi.org/10.1216/jca.2023.15.481","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139017679","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 TJURINA IDEALS OF HYPERSURFACE SINGULARITIES 关于超曲面奇点的tjurina理想
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2023-06-01 DOI: 10.1216/jca.2023.15.261
João Hélder Olmedo Rodrigues
{"title":"ON TJURINA IDEALS OF HYPERSURFACE SINGULARITIES","authors":"João Hélder Olmedo Rodrigues","doi":"10.1216/jca.2023.15.261","DOIUrl":"https://doi.org/10.1216/jca.2023.15.261","url":null,"abstract":"The Tjurina ideal of a germ of an holomorphic function $f$ is the ideal of $mathscr{O}_{mathbbm{C}^n,0}$ - the ring of those germs at $0inmathbbm{C}^n$ - generated by $f$ itself and by its partial derivatives. Here it is denoted by $T(f)$. The ideal $T(f)$ gives the structure of closed subscheme of $(mathbbm{C}^n,0)$ to the hypersurface singularity defined by $f$, being an object of central interest in Singularity Theory. In this note we introduce emph{$T$-fullness} and emph{$T$-dependence}, two easily verifiable properties for arbitrary ideals of germs of holomorphic functions. These two properties allow us to give necessary and sufficient conditions on an ideal $Isubset mathscr{O}_{mathbbm{C}^n,0}$, for the equation $I=T(f)$ to admit a solution $f$.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82575875","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
CHARACTERIZATION OF FERMAT HYPERSURFACES BY ABELIAN GROUPS 用阿贝尔群刻画费马超曲面
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2023-06-01 DOI: 10.1216/jca.2023.15.233
Taro Hayashi
{"title":"CHARACTERIZATION OF FERMAT HYPERSURFACES BY ABELIAN GROUPS","authors":"Taro Hayashi","doi":"10.1216/jca.2023.15.233","DOIUrl":"https://doi.org/10.1216/jca.2023.15.233","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76502156","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
A CHARACTERISATION OF LOCAL N-RINGS AND AN APPLICATION TO ABSTRACT HARMONIC ANALYSIS 局部n环的表征及其在抽象调和分析中的应用
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2023-06-01 DOI: 10.1216/jca.2023.15.287
B. Wilkens
{"title":"A CHARACTERISATION OF LOCAL N-RINGS AND AN APPLICATION TO ABSTRACT HARMONIC ANALYSIS","authors":"B. Wilkens","doi":"10.1216/jca.2023.15.287","DOIUrl":"https://doi.org/10.1216/jca.2023.15.287","url":null,"abstract":"A BSTRACT . A commutative ring with unity is called an N -ring if each of its ideals is contracted from an Noetherian extension ring. The chief result of the paper is a characterisation of local N -rings by their subdirectly irreducible quotients. The results are applied to characterise spectral synthesis on G -invariant subspaces of the space of complex valued functions on an Abelian group G .","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85507345","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
UNEXPECTED CURVES IN ℙ2, LINE ARRANGEMENTS, AND MINIMAL DEGREE OF JACOBIAN RELATIONS 未知的曲线，线的排列，以及雅可比矩阵关系的最小程度
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2023-03-01 DOI: 10.1216/jca.2023.15.15
A. Dimca
{"title":"UNEXPECTED CURVES IN ℙ2, LINE ARRANGEMENTS, AND MINIMAL DEGREE OF JACOBIAN RELATIONS","authors":"A. Dimca","doi":"10.1216/jca.2023.15.15","DOIUrl":"https://doi.org/10.1216/jca.2023.15.15","url":null,"abstract":"We reformulate a fundamental result due to Cook, Harbourne, Migliore and Nagel on the existence and irreduciblity of unexpected plane curves of a set of points Z in P2, using the minimal degree of a Jacobian syzygy of the defining equation for the dual line arrangement AZ . Several applications of this new approach are given. In particular, we show that the irreducible unexpected quintics may occur only when the set Z has the cardinality equal to 11 or 12, and describe five cases where this happens.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86750277","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
TORSION-FREE EXTENSIONS OF PROJECTIVE MODULES BY TORSION MODULES 通过扭转模对射影模的无扭转扩展
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2023-03-01 DOI: 10.1216/jca.2023.15.31
L. Fuchs
{"title":"TORSION-FREE EXTENSIONS OF PROJECTIVE MODULES BY TORSION MODULES","authors":"L. Fuchs","doi":"10.1216/jca.2023.15.31","DOIUrl":"https://doi.org/10.1216/jca.2023.15.31","url":null,"abstract":"We consider a generalization of a problem raised by P. Griffith [12] on abelian groups to modules over integral domains, and prove an analogue of a theorem of M. Dugas and J. Irwin [2]. Torsion modules T with the following property are characterized: if M is a torsion-free module and F is a projective submodule such that M/F ∼= T , then M is projective (Theorem 4.1). It is shown in Theorem 6.4 that for abelian groups whose cardinality is not cofinal with ω this is equivalent to being totally reduced in the sense of L. Fuchs and K. Rangaswamy [9]. The problem for valuation domains is also discussed, the results are similar to the case of abelian groups.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82859113","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
ATTACHED PRIMES OF LOCAL COHOMOLOGY MODULES OF COMPLEXES 复合体局部上同模的附加素数
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2023-03-01 DOI: 10.1216/jca.2023.15.75
Nguyen Minh Tri
{"title":"ATTACHED PRIMES OF LOCAL COHOMOLOGY MODULES OF COMPLEXES","authors":"Nguyen Minh Tri","doi":"10.1216/jca.2023.15.75","DOIUrl":"https://doi.org/10.1216/jca.2023.15.75","url":null,"abstract":". Let ( R, m ) be a local ring, Z a specialization closed subset of Spec R and X an R -complex with finitely generated homology and finite dimension. We show that Att R H dim X Z ( X ) = { p ∈ Supp R X | cd( Z , R/ p ) − inf X p = dim R X } . We also represent a generalization of Lichtenbaum-Hartshorne Vanishing Theorem for complexes of R -modules.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86007676","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
COMPANION VARIETIES FOR HESSE, HESSE UNION DUAL HESSE ARRANGEMENTS 黑塞的伴生品种，黑塞联合双黑塞排列
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2023-03-01 DOI: 10.1216/jca.2023.15.1
Pietro De Poi, G. Ilardi
{"title":"COMPANION VARIETIES FOR HESSE, HESSE UNION DUAL HESSE ARRANGEMENTS","authors":"Pietro De Poi, G. Ilardi","doi":"10.1216/jca.2023.15.1","DOIUrl":"https://doi.org/10.1216/jca.2023.15.1","url":null,"abstract":". Unexpected hypersurface is a name given an element to some particular linear system introduced around in [2], motivated by work of Di Gennaro, Ilardi and Vall`es and of Faenzi and Vall`es, and it is a field of great study since then. It attracts many people because of their close tights to various other areas of mathematics including vector bundles, arrangements of hyperplanes, geometry of projective varieties, etc. In this paper we continue the study about BMSS duality, of [3]. In [6], the authors introduced the concept of unexpected hypersurfaces and they explain the so-called BMSS duality showing that unexpected curves are in some sense dual to their tangent cones at their singular point. In this paper, we revisit the configuration of points associated to Hesse arrangement, Hesse union dual Hesse arrangement and we study the geometry of the associated varieties and their companions.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83889256","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
REDUCTIONS OF IDEALS IN PRÜFER RINGS prÜfer环中理想化约
IF 0.6 4区 数学
Journal of Commutative Algebra Pub Date : 2023-03-01 DOI: 10.1216/jca.2023.15.45
M. Jarrar, S. Kabbaj
{"title":"REDUCTIONS OF IDEALS IN PRÜFER RINGS","authors":"M. Jarrar, S. Kabbaj","doi":"10.1216/jca.2023.15.45","DOIUrl":"https://doi.org/10.1216/jca.2023.15.45","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89542413","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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