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Cubo (Temuco)
versión On-line ISSN 0719-0646
Cubo vol.24 no.2 Temuco ago. 2022
http://dx.doi.org/10.56754/0719-0646.2402.0291
Articles
Graded weakly 1-absorbing prime ideals
1
http://orcid.org/0000-0003-0739-1449
2
http://orcid.org/0000-0003-1622-786X
1Department of Mathematics, Marmara University, Istanbul, Turkey. utekir@marmara.edu.tr
2Department of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey. suat.koc@medeniyet.edu.tr
3Department of Mathematics, Yarmouk University, Jordan. rrashid@yu.edu.jo
4Department of Mathematics, Yildiz Technical University, Istanbul, Turkey. edyildiz@yildiz.edu.tr
In this paper, we introduce and study graded weakly 1-absorbing prime ideals in graded commutative rings. Let G be a group and R be a G-graded commutative ring with a nonzero identity 1 ≠ 0. A proper graded ideal P of R is called a graded weakly 1-absorbing prime ideal if for each nonunits x, y, z ∈ h(R) with 0 ≠ xyz ∈ P, then either xy ∈ P or z ∈ P. We give many properties and characterizations of graded weakly 1-absorbing prime ideals. Moreover, we investigate weakly 1-absorbing prime ideals under homomorphism, in factor ring, in rings of fractions, in idealization.
Keywords and Phrases: graded ideal; 1-absorbing prime ideal; weakly 1-absorbing prime ideal; graded weakly 1-absorbing prime ideal
En este artículo, introducimos y estudiamos ideales primos débilmente 1-absorbentes en anillos conmutativos gradados. Sea G un grupo y R un anillo conmutativo G-gradado con identidad no cero 1 ≠ 0. Un ideal gradado propio P de R se llama ideal primo gradado débilmente 1-absorbente si para cualquiera x, y, z ∈ h(R) no-unidades con 0 ≠ xyz ∈ P, entonces o bien xy ∈ P o z ∈ P. Entregamos muchas propiedades y caracterizaciones de ideales primos gradados débilmente 1-absorbentes. Más aún, investigamos ideales primos débilmente 1-absorbentes bajo homomorfismo, en anillos cociente, en anillos de fracciones, en idealización.
Acknowledgments
The authors would like to thank the referee for his/her valuable comments that improved the paper.
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Accepted: June 06, 2022; Received: November 24, 2021
This is an open-access article distributed under the terms of the Creative Commons Attribution License
