On Graded 2-Absorbing and Graded Weakly 2-Absorbing Ideals of a Commutative Ring

Sadegh Rahimi NAGHANİ [1] , Hosein Fazaeli MOGHİMİ [2]


Let G be a group with identity e and R be a G-graded commutative ring with 1 6= 0. In this paper, we study the graded versions of 2-absorbing and weakly 2-absorbing ideals which are generalizations of the graded prime and graded weakly prime ideals, respectively. A graded proper ideal I of R is called a graded 2- absorbing (resp. graded weakly 2-absorbing) ideal if whenever abc ∈ I (resp. 0 != abc ∈ I) for homogeneous elements a,b, c ∈ R, then ab ∈ I or ac ∈ I or bc ∈ I. It is clear that a graded ideal which is a 2-absorbing ideal, is a graded 2-absorbing ideal, but we show that the converse is not true in general. It is proved that if I = ⊕g∈GIg is a graded weakly 2-absorbing ideal of R, then either I is a 2-absorbing ideal of R or I3g = (0) for all g ∈ G. It is also shown that if I = ⊕i∈GIg is a graded weakly 2-absorbing ideal of R, then for each g ∈ G, either Ig is a 2-absorbing Re-submodule of Rg or (Ig :Re Rg) 2 Ig = 0.

Graded prime ideal, graded 2-absorbing ideal, graded weakly 2-absorbing ideal
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Konular Mühendislik
Bölüm Makaleler
Yazarlar

Yazar: Sadegh Rahimi NAGHANİ

Yazar: Hosein Fazaeli MOGHİMİ

Tarihler

Yayımlanma Tarihi : 1 Kasım 2016

Bibtex @araştırma makalesi { cankujse344501, journal = {Cankaya University Journal of Science and Engineering}, issn = {}, eissn = {2564-7954}, address = {}, publisher = {Çankaya Üniversitesi}, year = {2016}, volume = {13}, pages = { - }, doi = {}, title = {On Graded 2-Absorbing and Graded Weakly 2-Absorbing Ideals of a Commutative Ring}, key = {cite}, author = {Naghani̇, Sadegh Rahimi and Moghi̇mi̇, Hosein Fazaeli} }
APA Naghani̇, S , Moghi̇mi̇, H . (2016). On Graded 2-Absorbing and Graded Weakly 2-Absorbing Ideals of a Commutative Ring . Cankaya University Journal of Science and Engineering , 13 (2) , . Retrieved from https://dergipark.org.tr/tr/pub/cankujse/issue/31473/344501
MLA Naghani̇, S , Moghi̇mi̇, H . "On Graded 2-Absorbing and Graded Weakly 2-Absorbing Ideals of a Commutative Ring" . Cankaya University Journal of Science and Engineering 13 (2016 ): <https://dergipark.org.tr/tr/pub/cankujse/issue/31473/344501>
Chicago Naghani̇, S , Moghi̇mi̇, H . "On Graded 2-Absorbing and Graded Weakly 2-Absorbing Ideals of a Commutative Ring". Cankaya University Journal of Science and Engineering 13 (2016 ):
RIS TY - JOUR T1 - On Graded 2-Absorbing and Graded Weakly 2-Absorbing Ideals of a Commutative Ring AU - Sadegh Rahimi Naghani̇ , Hosein Fazaeli Moghi̇mi̇ Y1 - 2016 PY - 2016 N1 - DO - T2 - Cankaya University Journal of Science and Engineering JF - Journal JO - JOR SP - EP - VL - 13 IS - 2 SN - -2564-7954 M3 - UR - Y2 - 2020 ER -
EndNote %0 Cankaya University Journal of Science and Engineering On Graded 2-Absorbing and Graded Weakly 2-Absorbing Ideals of a Commutative Ring %A Sadegh Rahimi Naghani̇ , Hosein Fazaeli Moghi̇mi̇ %T On Graded 2-Absorbing and Graded Weakly 2-Absorbing Ideals of a Commutative Ring %D 2016 %J Cankaya University Journal of Science and Engineering %P -2564-7954 %V 13 %N 2 %R %U
ISNAD Naghani̇, Sadegh Rahimi , Moghi̇mi̇, Hosein Fazaeli . "On Graded 2-Absorbing and Graded Weakly 2-Absorbing Ideals of a Commutative Ring". Cankaya University Journal of Science and Engineering 13 / 2 (Kasım 2016): - .
AMA Naghani̇ S , Moghi̇mi̇ H . On Graded 2-Absorbing and Graded Weakly 2-Absorbing Ideals of a Commutative Ring. Cankaya University Journal of Science and Engineering. 2016; 13(2): -.
Vancouver Naghani̇ S , Moghi̇mi̇ H . On Graded 2-Absorbing and Graded Weakly 2-Absorbing Ideals of a Commutative Ring. Cankaya University Journal of Science and Engineering. 2016; 13(2): -.