{"title":"ON THE INTEGRAL CLOSURE OF RADICAL TOWERS IN MIXED CHARACTERISTIC","authors":"Daniel Katz, Prashanth Sridhar","doi":"10.1216/jca.2023.15.543","DOIUrl":"https://doi.org/10.1216/jca.2023.15.543","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"598 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139020901","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 THE SECTIONAL GENERA AND COHEN–MACAULAY RINGS","authors":"Shinya Kumashiro, Hoang Le Truong, Hoang Ngoc Yen","doi":"10.1216/jca.2023.15.577","DOIUrl":"https://doi.org/10.1216/jca.2023.15.577","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"15 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139023606","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":"LATTICE DECOMPOSITION OF MODULES OVER COMMUTATIVE RINGS","authors":"Josefa M. García, Pascual Jara, Eva Santos","doi":"10.1216/jca.2023.15.497","DOIUrl":"https://doi.org/10.1216/jca.2023.15.497","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"44 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139015232","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":"Author Index to Volume 15 (2023)","authors":"","doi":"10.1216/jca.2023.15.609","DOIUrl":"https://doi.org/10.1216/jca.2023.15.609","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"224 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139018584","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":"STRUCTURE OF THE KERNEL OF A LOCALLY NILPOTENT DERIVATION ON AN AFFINE NORMAL DOMAIN","authors":"S. M. Bhatwadekar, Jatin T. Majithia","doi":"10.1216/jca.2023.15.457","DOIUrl":"https://doi.org/10.1216/jca.2023.15.457","url":null,"abstract":"","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":"80 ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138992777","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}
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":"90 8","pages":""},"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}
{"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":"88 8","pages":""},"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}
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 $f$.
{"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":"44 1","pages":""},"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}
{"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":"440 1","pages":""},"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}
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 .
{"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":"10 1","pages":""},"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}
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