On Graded 2-Prime Ideals

Malik Bataineh and Rashid Abu-Dawwas
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Malik Bataineh: Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan
Rashid Abu-Dawwas: Department of Mathematics, Yarmouk University, Irbid 22110, Jordan

Mathematics, 2021, vol. 9, issue 5, 1-10

Abstract: The purpose of this paper is to introduce the concept of graded 2-prime ideals as a new generalization of graded prime ideals. We show that graded 2-prime ideals and graded semi-prime ideals are different. Furthermore, we show that graded 2-prime ideals and graded weakly prime ideals are also different. Several properties of graded 2-prime ideals are investigated. We study graded rings in which every graded 2-prime ideal is graded prime, we call such a graded ring a graded 2-P-ring. Moreover, we introduce the concept of graded semi-primary ideals, and show that graded 2-prime ideals and graded semi-primary ideals are different concepts. In fact, we show that graded semi-primary, graded 2-prime and graded primary ideals are equivalent over Z -graded principal ideal domain.

Keywords: graded prime ideal; graded primary ideal; graded semi-primary ideals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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