Trivial Extensions Defined by Coherent-like Conditions

Abstract

This paper investigates coherent-like conditions and related properties that a trivial extension R ≔ A ∝ E might inherit from the ring A for some classes of modules E. It captures previous results dealing primarily with coherence, and also establishes satisfactory analogues of well-known coherence-like results on pullback constructions. Our results generate new families of examples of rings (with zerodivisors) subject to a given coherent-like condition.

Key Words:

• Trivial extension
• Pullback
• Coherence
• Finite conductor ring
• Quasi-coherent ring
• G-GCD ring
• n-coherence
• (n, d)-ring

Mathematics Subject Classification:

• Primary 13Agg
• Secondary 13D05, 13B02

Acknowledgment

The first author was supported by KFUPM under project #MS/TRIVIAL/224.

Notes

^#Communicated by I. Swanson.