Let R and S be arbitrary rings and let CSR be a semidualizing bimodule, and let 𝒜 C⁢(R op)
and ℬ C⁢(R) be the Auslander and Bass classes, respectively. Then both pairs (𝒜 C⁢(R …

We study the concepts of the 𝒫 C-projective and the ℐ C-injective dimensions of a module in
the noncommutative case, weakening the condition of C being semidualizing. We give 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 …

We investigate the notion of the C-projective dimension of a module, where C is a
semidualizing module. When C= R, this recovers the standard projective dimension. We …

Weak as-modules share some of the properties of as-modules. For example, we prove that if
M is a weak CS-module which satisfies the ascending chain condition on essential …

It is shown that every finitely generated projective module PR over a semiprime ring R has
the smallest FI-extending essential module extension (called the absolute FI-extending hull …

If M denotes the class of unitary left modules over a ring R, then each subclass# ofM
determines two subclasses ofJt—the relative projectivity class and the relative injectivity …

A submodule N of a right R-module M is called coneat if for every simple right R-module S,
any homomorphism $ N {\rightarrow} S $ can be extended to a homomorphism $ M …

Over integral domains, we characterize modules of finite weak dimension⩽ n in terms of h-
divisible pure-injective modules (Theorems 2.1 and 2.2). We compare various classes of h …

A finitely generated module C over a commutative noetherian ring R is semidualizing if Hom
R (C, C)≅ R and for all i≥ 1. For certain local Cohen–Macaulay rings (R, 𝔪), we verify the …