Gorenstein Dimensions over Some Rings of the Form \(R \oplus C\)

Given a semidualizing module \(C\) over a commutative noetherian ring, Holm and J\o{}rgensen investigate some connections between \(C\)-Gorenstein dimensions of an \(R\)-complex and Gorenstein dimensions of the same complex viewed as a complex over the "trivial extension" \(R \ltimes C\)....

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Bibliographic Details
Published inarXiv.org
Main Author Pye Phyo Aung
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.03.2015
Subjects
Rings (mathematics)
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Summary:Given a semidualizing module \(C\) over a commutative noetherian ring, Holm and J\o{}rgensen investigate some connections between \(C\)-Gorenstein dimensions of an \(R\)-complex and Gorenstein dimensions of the same complex viewed as a complex over the "trivial extension" \(R \ltimes C\). We generalize some of their results to a certain type of retract diagram. We also investigate some examples of such retract diagrams, namely D'Anna and Fontana's amalgamated duplication and Enescu's pseudocanonical cover.
ISSN:2331-8422
DOI:10.48550/arxiv.1408.1123