$S$-Prime and $S$-maximal ideals in trivial ring extensions of commutative rings

Hwankoo Kim, Najib Mahdou, El Houssaine Oubouhou

This paper explores the study of $S$-prime and $S$-maximal ideals in the context of trivial ring extensions $A⋉M$. Through counterexamples, we demonstrate that $S$-prime (r…