Moroccan Journal of Algebra and Geometry with Applications
On graded strongly quasi primary ideals
Ranya Abdullah, Rashid Abu-Dawwas, Suat Koç, Ünsal Tekir and Eda Yıldız
Department of Mathematics, Yarmouk University, Irbid, Jordan
Department of Mathematics, Yarmouk University, Irbid, Jordan
Department of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey
Department of Mathematics, Marmara University, Istanbul, Turkey
Department of Mathematics, Yildiz Technical University, Istanbul, Turkey
Pages 409-417 | Received 13 August 2022, Accepted 28 October 2022, Published 06 December 2022
Abstract
In this article, we introduce graded strongly quasi primary ideals which is an intermediate class of graded primary ideals and graded quasi primary ideals. Let G be a group with identity e, R be a G-graded commutative ring with nonzero unity 1 and P be a proper graded ideal of R. Then P is said to be a graded strongly quasi primary ideal if xy \in P for x,y \in h(R) implies either x^2 \in P or y^n \in P (x^n \in P or y^2 \in P) for some n \in \mathbb{N}. We give many properties of graded strongly quasi primary ideals and investigate the relations between graded strongly quasi primary ideals and other classical graded ideals such as graded primary, graded 2-prime and graded quasi primary ideals.
Keywords: Graded strongly quasi primary ideals; graded primary ideals; graded 2-prime ideals; graded quasi primary ideals.
MSC numbers: Primary 13A02, Secondary 16W50.
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