When every Gorenstein projective (resp. flat) module is strongly Gorenstein projective (resp. flat)
Najib Mahdou, Mohamed Tamekkante
TL;DR
This paper explores rings where all Gorenstein projective or flat modules are strongly Gorenstein, providing examples with various Gorenstein global dimensions to extend previous characterizations.
Contribution
It extends the study of rings by characterizing those where Gorenstein modules are strongly Gorenstein, offering new examples across different Gorenstein global dimensions.
Findings
Identification of rings with all Gorenstein modules strongly Gorenstein
Examples of rings with various Gorenstein global dimensions satisfying this condition
Extension of previous work on strongly Gorenstein modules
Abstract
In \cite{Ouarghi}, the authors discuss the rings over which all modules are strongly Gorenstein projective. In this paper, we are interesting to an extension of this idea. Thus, we discuss the rings over which every Gorenstein projective (resp. flat) module is strongly Gorenstein projective (resp, flat). Our aim is to give examples of rings with different Gorenstein global dimension satisfied this condition.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Commutative Algebra and Its Applications