For a finite-dimensional algebra Λ and a nonnegative integer n, we characterize when the
set tilt n Λ of additive equivalence classes of tilting modules with projective dimension at …

In this paper, our primary focus is on investigating the extension dimensions of syzygy
module categories associated with Artin algebras, particularly under various equivalences …

Auslander and Bridger [Stable module theory, Memoirs of the American Mathematical
Society, No. 94, American Mathematical Society, Providence, RI, 1969] introduced the …

Let RR be an Artin algebra. Under certain Auslander‐type conditions, we give some
equivalent characterizations of (weakly) Gorenstein algebras in terms of the properties of …

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 …

Let R be a ring and 𝒬 be a finite and acyclic quiver. We present an explicit formula for the
injective envelopes and projective precovers in the category Rep (𝒬, R) of representations of …

1. Introduction Throughout this paper, all rings are associative rings with units. For a ring R, we
use Mod R to denote the cate Page 1 EXTENSION CLOSURE OF ADJOINT COTORSIONFREE …

Under some strong cograde conditions, we obtain two different filtrations of modules in terms
of the properties of cotransposes of modules with respect to a semidualizing bimodule. Then …

Let R be a left and right Noetherian ring and n, k be any non-negative integers. R is said to
satisfy the Auslander-type condition G n (k) if the right flat dimension of the (i+ 1)-th term in a …

In this paper we mainly study the homological properties of dual modules over k-Gorenstein
rings. For a right quasi k-Gorenstein ring Λ, we show that the right self-injective dimension of …