Weak dimension of FP-injective modules over chain rings

TL;DR

This paper proves that over certain chain rings, the weak dimension of FP-injective modules is bounded above by 2, extending understanding of module dimensions in ring theory.

Contribution

It establishes a uniform bound on the weak dimension of FP-injective modules over specific classes of chain rings, including Archimedean and non-semicoherent rings.

Findings

Weak dimension of FP-injective modules is ≤ 2 over Archimedean chain rings.

Weak dimension of FP-injective modules is ≤ 2 over non-semicoherent chain rings.

Provides new bounds on module dimensions in chain ring contexts.

Abstract

It is proven that the weak dimension of each FP-injective module over a chain ring which is either Archimedean or not semicoherent is less or equal to 2.