S-radical of an ideal and strongly S-n ideals

Abstract

In this paper, we investigate some properties of S-radical which is a generalization of classical radical. We moreover, determine S-radical of several types of ideals. Then we introduce the notion of strongly S-n-ideals that is an intermediate class between n-ideals and S-n-ideals. We investigate many properties of this class of ideals with illustrative examples. Finally, we obtain some results related to strongly S-n-ideals in amalgamated algebra.