On 1-absorbing delta-primary ideals

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El Khalfi A., Mahdou N., Tekir Ü., Koç S.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, vol.29, no.3, pp.135-150, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.2478/auom-2021-0038
  • Journal Name: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.135-150
  • Keywords: 1-absorbing prime ideal, 1-absorbing delta-primary ideal, beta-primary ideal, trivial extension

Abstract

Let R be a commutative ring with nonzero identity. Let J(R) be the set of all ideals of R and let delta : J(R) - -> J(R) be a function. Then delta is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J subset of I, we have L subset of delta(L) and delta(J) subset of delta(I). Let delta be an expansion function of ideals of R. In this paper, we introduce and investigate a new class of ideals that is closely related to the class of delta-primary ideals. A proper ideal I of R is said to be a 1-absorbing delta-primary ideal if whenever nonunit elements a, b, c is an element of R and abc is an element of I, then ab is an element of I or c is an element of delta(I). Moreover, we give some basic properties of this class of ideals and we study the 1-absorbing delta-primary ideals of the localization of rings, the direct product of rings and the trivial ring extensions.