ARTICLE | doi:10.20944/preprints202108.0479.v1
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Graded weakly prime ideals; graded S-prime ideals; graded weakly S-prime ideals.
Online: 25 August 2021 (08:39:01 CEST)
Let R be a commutative graded ring with unity, S be a multiplicative subset of homogeneous elements of R and P be a graded ideal of R such that P\bigcap S=\emptyset In this article, we introduce several results concerning graded S-prime ideals. Then we introduce the concept of graded weakly S-prime ideals which is a generalization of graded weakly prime ideals. We say that P is a graded weakly S-prime ideal of R if there exists s\in S such that for all x, y\in h(R), if 0\neq xy\in P, then sx\in P or sy\in P. We show that graded weakly S-prime ideals have many acquaintance properties to these of graded weakly prime ideals.