On weak P-coherent rings

Abstract

In this paper, we introduce a generalization of the well-known notion of weak coherent rings, which we call weak [Formula: see text]-coherent rings. We investigate the stability of this property under direct products and homomorphic image, and its transfer to various contexts of constructions such as trivial ring extensions and amalgamated algebras along an ideal. We conclude with various examples of weak [Formula: see text]-coherent rings.