Abstract

The concepts of prime ideals and corresponding radicals play an important role in the study of nearrings. In this paper, we define different prime strong ideals of a seminearring $S$ and study the corresponding prime radicals. In particular, we prove that $P_e=S\mid P_e(S)=S $ is a Kurosh-Amitsur radical class where $P_{e}(S)$ denotes the intersection of equiprime strong ideals of $S$.

Keywords: Seminearring; strong ideal; radical.

MSC: 16Y30, 16Y60

Pages:  243$-$256     

Volume  72 ,  Issue  3 ,  2020