Online First Articles
Rings whose indecomposable modules are pure-projective or pure-injective
DOI:
10.2989/16073606.2025.2457684
Keywords:
13C05, 13C13, 13F05, 13F30, 16L30, 16S50, Pure-projective module, pure-injective module, maximal valuation ring, discrete valuation domain of rank one, Gelfand ring, clean ring, arithmetical ring,
Abstract
Let be the class of rings for which every indecomposable right module is pure-projective or pure-injective. When R is a Noetherian local commutative ring of maximal ideal P, it is proven that R ∈ if and only if R is either an artinian valuation ring or a discrete valuation domain of rank one with rank where is the completion of R in its P-adic topology. Let R be a commutative ring. Then R ∈ if and only if R is a clean arithmetical ring with RP
∈ for each maximal ideal P of R. Moreover, R is a semi-perfect ring when it is Noetherian. Some examples of commutative rings of the class are given.
Get new issue alerts for Quaestiones Mathematicae
