Let A be a ring and M an AA-bimodule. Any left module over the trivial extension A⋉ M is
corresponds to a pair (X, ϕ) where X is a left A-module and ϕ is an A-morphism from M⊗ AX …

Notes on Strongly n-Gorenstein Projective, Injective and Flat Modules Email Alert | Rss | Fig/Tab
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We consider a ring R such that the class of Gorenstein injective modules is closed under
direct limits. We prove that the class of dg-Gorenstein injective complexes is covering in Ch …

1. Preliminaries. In this note we introduce a new tensor product functor in the category of
complexes. We show that this tensor product is left adjoint to the Hom functor properly …

Let R be a ring with identity and C (R) denote the category of complexes of R-modules. In
this paper we study the homotopy categories arising from projective (resp. injective) …

The study of rings and modules with homological criteria is a cornerstone of commutative
algebra. Let $ R $ be a commutative Noetherian ring with identity (not necessarily local) and …

Let R be a commutative Noetherian ring and let I be an ideal of R. In this paper, we study the
amalgamated duplication ring R⋈ I which is introduced by D'Anna and Fontana. It is shown …

Abstract Let $ A $ and $ B $ be rings, $ U $ a $(B, A) $-bimodule, and $ T=\left (\begin
{smallmatrix} A & 0\\U & B\\\end {smallmatrix}\right) $ the triangular matrix ring. In this paper …

We describe the Gorenstein derived categories of Gorenstein rings via the homotopy
categories of Gorenstein injective modules. We also introduce the concept of Gorenstein …

Suppose $ R $ is a $\mathbb {Q} $-Gorenstein $ F $-finite and $ F $-pure ring of prime
characteristic $ p> 0$. We show that if $ I\subseteq R $ is a compatible ideal (with all $ p^{-e} …