- International Electronic Journal of Algebra
- Vol: 30 Issue: 30
- A NOTE ON SATURATED MULTIPLICATIVELY CLOSED SETS
A NOTE ON SATURATED MULTIPLICATIVELY CLOSED SETS
Authors : Mehdi Badie
Pages : 260-268
Doi:10.24330/ieja.969924
View : 9 | Download : 4
Publication Date : 2021-07-17
Article Type : Research
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