Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Characterizations of Graded Rings Over Which Every Graded Semi-primary Ideal is Graded 1-absorbing Primary

Version 1 : Received: 24 August 2021 / Approved: 26 August 2021 / Online: 26 August 2021 (09:57:50 CEST)

How to cite: Melhem, A.; Bataineh, M.; Abu-Dawwas, R. Characterizations of Graded Rings Over Which Every Graded Semi-primary Ideal is Graded 1-absorbing Primary. Preprints 2021, 2021080503 (doi: 10.20944/preprints202108.0503.v1). Melhem, A.; Bataineh, M.; Abu-Dawwas, R. Characterizations of Graded Rings Over Which Every Graded Semi-primary Ideal is Graded 1-absorbing Primary. Preprints 2021, 2021080503 (doi: 10.20944/preprints202108.0503.v1).

Abstract

Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero unity $1$. Graded semi-primary and graded $1$-absorbing primary ideals have been investigated and examined by several authors as generalizations of graded primary ideals. However, these three concepts are different. In this article, we characterize graded rings over which every graded semi-primary ideal is graded $1$-absorbing primary and graded rings over which every graded $1$-absorbing primary ideal is graded primary.

Keywords

Graded 1-absorbing primary ideals; graded primary ideals; graded semi-primary ideals.

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