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S-COHERENT PROPERTY IN TRIVIAL EXTENSION AND IN AMALGAMATED DUPLICATION
Mohamed Chhiti,Salah Eddine Mahdou Korean Mathematical Society 2023 대한수학회논문집 Vol.38 No.3
Bennis and El Hajoui have defined a (commutative unital) ring R to be S-coherent if each finitely generated ideal of R is a S-finitely presented R-module. Any coherent ring is an S-coherent ring. Several examples of S-coherent rings that are not coherent rings are obtained as byproducts of our study of the transfer of the S-coherent property to trivial ring extensions and amalgamated duplications.
When every finitely generated regular ideal is finitely presented
Mohamed Chhiti,Salah Eddine Mahdou 대한수학회 2024 대한수학회논문집 Vol.39 No.2
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.