Let 𝒜 be an abelian category having enough projective and injective objects, and let 𝒯 be
an additive subcategory of 𝒜 closed under direct summands. A known assertion is that in a …

We introduce relative preresolving subcategories and precoresolving subcategories of an
abelian category and define homological dimensions and codimensions relative to these …

Let R and S be rings and RωS a semidualizing bimodule. We introduce and study the
adjoint cotransposes of modules and adjoint n-ω-cotorsionfree modules. We show that the …

Let R and S be rings and RCS a semidualizing bimodule. We show that the supremum of the
C-projective dimensions of C-flat left R-modules is less than or equal to that for left R …

Given an additive category C and an integer n≥ 2. The higher differential additive category
consists of objects X in C equipped with an endomorphism ϵX satisfying ϵn X= 0. Let R be a …

Let $ R $ and $ S $ be rings and $ _S\omega_R $ a semidualizing bimodule. For a subclass
$\mathcal {T} $ of the class of $\omega $-coreflexive modules and $ n\geq 1$, we introduce …

SEMIDUALIZING MODULES AND TRIVIAL RING EXTENSIONS Lixin Mao Abstract 1.
Introduction Throughout this paper, R is a commutative a Page 1 L. MAO KODAI MATH. J. 47 …

Let R, S be arbitrary associative rings and RCS a semidualizing bimodule. We give some
equivalent characterizations for R being left coherent (and right perfect) rings, left …

Let R and S be rings and RωS a semidualizing bimodule. We investigate when the double
functor TorS i (ω, Exti R (ω,−)) preserves epimorphisms and the double functor Exti R (ω …

As the dual of the Auslander transpose and the resulting k-torsionfree module, the
cotranspose and k-cotorsionfree module with respect to a semidualizing bimodule have …