An extension of a theorem of Frobenius and Stickelberger to modules of projective dimension one over a factorial domain

Let R be a Cohen–Macaulay ring. A quasi-Gorenstein R-module is an R-module such that the grade of the module and the projective dimension of the module are equal and the canonical module of the module is isomorphic to the module itself. After discussing properties of finitely generated quasi-Gorenst...

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Bibliographic Details
Published inJournal of pure and applied algebra Vol. 223; no. 2; pp. 626 - 633
Main Authors Brennan, Joseph P., York, Alexander
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2019
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secondary
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Summary:Let R be a Cohen–Macaulay ring. A quasi-Gorenstein R-module is an R-module such that the grade of the module and the projective dimension of the module are equal and the canonical module of the module is isomorphic to the module itself. After discussing properties of finitely generated quasi-Gorenstein modules, it is shown that this definition allows for a characterization of diagonal matrices of maximal rank over a Cohen–Macaulay factorial domain R extending a theorem of Frobenius and Stickelberger to modules of projective dimension 1 over a commutative factorial Cohen–Macaulay domain.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2018.04.011