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arXiv · 1408.1123

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

Pye Phyo Aung
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Abstract

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.

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Pye Phyo Aung. 2014-08-05. Gorenstein Dimensions over Some Rings of the Form $R \oplus C$. https://doi.org/10.1142/s0219498816500432

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