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KOÇ, SUAT

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Subject: 1-absorbing prime ideal ×

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Now showing 1 - 3 of 3
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    PublicationOpen Access
    On phi-1-absorbing prime ideals
    (SPRINGER HEIDELBERG, 2021-12) KOÇ, SUAT; Yildiz, Eda; Tekir, Unsal; Koc, Suat
    In this paper, we introduce phi-1-absorbing prime ideals in commutative rings. Let R be a commutative ring with a nonzero identity 1 not equal 0 and phi : I(R) -> I(R) boolean OR {theta} be a function where I( R) is the set of all ideals of R. A proper ideal I of R is called a phi-1-absorbing prime ideal if for each nonunits x, y, z is an element of R with xyz is an element of I - phi(I), then either xy is an element of I or z is an element of I. In addition to give many properties and characterizations of phi-1-absorbing prime ideals, we also determine rings in which every proper ideal is phi-1-absorbing prime.
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    PublicationOpen Access
    On weakly 1-absorbing prime ideals
    (SPRINGER-VERLAG ITALIA SRL, 2021-03-14) KOÇ, SUAT; Koc, Suat; Tekir, Unsal; Yildiz, Eda
    This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let A be a commutative ring with a nonzero identity 1 not equal 0. A proper ideal P of A is said to be a weakly 1-absorbing prime ideal if for every nonunits x, y, z. A with 0 not equal xyz. P, then xy is an element of P or z is an element of P. In addition to give many properties and characterizations of weakly 1-absorbing prime ideals, we also determine rings in which every proper ideal is weakly 1-absorbing prime. Furthermore, we investigate weakly 1-absorbing prime ideals in C( X), which is the ring of continuous functions of a topological space X.
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    PublicationOpen Access
    On 1-absorbing delta-primary ideals
    (OVIDIUS UNIV PRESS, 2021-11-01) KOÇ, SUAT; El Khalfi, Abdelhaq; Mahdou, Najib; Tekir, Unsal; Koc, Suat
    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.