Characterizations of rings via the decompositions of cyclic modules
Abstract
A module N is said to satisfy condition (*) if N has the form ⊕Ni, where each module Ni is either projective, CS, or has finite uniform dimension. Let M be a cyclic module. It is shown that every factor of M has finite uniform dimension if and only if every cyclic subfactor of M satisfies (*). As an application, we will provide criteria to dicide when a WV-ring is right Noetherian. In particular, we will prove that a WV-ring R is right Noetherian if and only if every cyclic R-module has the form ⊕Ci, where each module Ci is either projective, CS, or Noetherian. In addition, we will prove that a ring R is right Noetherian if every R-module satisfies (*).
Fields of Study & Subjects
Rings
Modules
and Algebras
Algebraic structures and combinatorial models
Advanced Algebra and Logic
Publication details
- Journal / source
- Communications in Algebra
- Volume
- 54
- Issue
- 11
- Pages
- 3456–3464
- Publication date
- 2 January 2026
- Language
- EN