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.
Konular | Mühendislik |
---|---|
Bölüm | Makaleler |
Yazarlar | |
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): -. |