Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

On Graded Weakly S-Prime Ideals

Version 1 : Received: 24 August 2021 / Approved: 25 August 2021 / Online: 25 August 2021 (08:39:01 CEST)

How to cite: Saber, H.; Alraqad, T.; Abu-Dawwas, R.; Shtayat, H.; Hamdan, M. On Graded Weakly S-Prime Ideals. Preprints 2021, 2021080479 (doi: 10.20944/preprints202108.0479.v1). Saber, H.; Alraqad, T.; Abu-Dawwas, R.; Shtayat, H.; Hamdan, M. On Graded Weakly S-Prime Ideals. Preprints 2021, 2021080479 (doi: 10.20944/preprints202108.0479.v1).

Abstract

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.

Keywords

Graded weakly prime ideals; graded S-prime ideals; graded weakly S-prime ideals.

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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