Communications of the
Korean Mathematical Society CKMS

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.

Keywords: $S$-coherence, $S$-finitely presented, $S$-finite, trivial ring extension, amalgamation algebra along an ideal

MSC numbers: Primary 13A15, 13B99, 13E15