Suppose (R, m) and (S, n) are commutative Noetherian local rings and ϕ: R→ S is a flat
local homomorphism with the property that the induced homomorphism R/m→ S/mS is …

While a module is pseudo-injective if and only if it is automorphism-invariant, it was not
known whether automorphism-invariant modules are tight. It is shown that weakly …

Let (R, 𝔪) be a Noetherian local ring of dimension d≥ 1 and let M be a nonzero finitely
generated R-module. Let n be a positive integer and let x 1,…, xn∈ 𝔪 be an M-regular …

In this paper, we introduce an X-precover completing domain X− 1 (L), with L being a class
of modules and not necessarily a single module, and then investigate when every module in …

We study direct-sum decompositions of RD-projective modules. In particular, we investigate
the rings over which every RD-projective right module is a direct sum of cyclically presented …

Abstract Let (R,\frakm) be a commutative Noetherian complete local ring and let I be a
proper ideal of R such that the category of all I-cofinite R-modules is an Abelian subcategory …

Almost N-projective modules and generalized N-projective modules play an important role
in the study of lifting modules and artinian rings. In this paper, we study a relationship …

Abstract Given modules $ A_ {R} $ and $ _ {R} B $, $ _ {R} B $ is called absolutely $ A_ {R}
$-pure if for every extension $ _ {R} C $ of $ _ {R} B $, $ A\otimes B\rightarrow A\otimes C …

A general principle suggests that" anything flat is a directed colimit of countably presentable
flats". In this paper, we consider resolutions and coresolutions of modules over a countably …

Let R be a commutative semilocal ring and U be the minimal injective cogenerator in the
category of R-modules. If R is almost noetherian, ie, each non-minimal prime ideal of R is …