Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce a weak version of coherent that we call regular coherent property. A ring is called regular coherent, if every finitely generated regular ideal is finitely presented. We investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as trivial ring extensions, pullbacks and amalgamated. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.

Keywords: Regular ideal, regular coherent ring, trivial ring extension, pullbacks, amalgamation

MSC numbers: 13A15, 13B99, 13E15