On pseudo-absorbing primary multiplication modules over pullback rings

TL;DR

This paper classifies indecomposable pseudo-absorbing primary multiplication modules with finite-dimensional top over pullback rings of valuation domains, extending Levy's classification to a new module class.

Contribution

It provides a complete classification of these modules over pullback of valuation domains and links them to pure-injective modules, advancing module theory over such rings.

Findings

Complete classification of modules over pullback of valuation domains.

Established connection between pseudo-absorbing modules and pure-injective modules.

Extended Levy's classification to a broader module class.

Abstract

A famous result due to L. S. Levy provides a classification of all finitely generated indecomposable modules over Dedekind-like rings. This motivates us to outline an approach to the classification of indecomposable pseudo-absorbing primary multiplication modules with finite-dimensional top over certain kinds of pullback rings. In this paper, we give a complete classification, up to isomorphism, of all indecomposable pseudo-absorbing primary multiplication modules with finite-dimensional top over a pullback of two valuation domains with the same residue field. We also find a connection between pseudo-absorbing primary multiplication modules and pure-injective modules over such domains.