A NOTE ON SATURATED MULTIPLICATIVELY CLOSED SETS

Authors : Mehdi BADIE

Pages : 260-268

Doi:10.24330/ieja.969924

View : 13 | Download : 10

Publication Date : 2021-07-17

Article Type : Research Paper

Abstract :In this paper, we introduce and study $ \mathcal{H}_Y $-s.m.c. and strong $ \mathcal{H}_Y $-s.m.c. sets and give some connections between them and lattice ideals of $ \mathcal{H}_Y $. Also, we introduce an ideal $ R_S $, for each subset set $ S $ of a ring $ R $. We prove a ring $ R $ is a Gelfand ring if and only if $ R_S $ is an intersection of maximal ideals, for every s.m.c. set $ S $ of $ R $.
Keywords : mathcal H Y ideal, mathcal H Y saturated multiplicatively closed set, closed ideal, C X, , maximal ideal