On graded Jgr-classical 2-absorbing submodules of graded modules over graded commutative rings

• Autorzy: Al-Zoubi Khaldoun , Alghueiri Shatha

Identyfikatory

DOI

10.1515/dema-2021-0015

• Języki publikacji: EN

Abstrakty

EN

Let G be an abelian group with identitye. Let R be a G-graded commutative ring with identity 1, and M be a graded R-module. In this paper, we introduce the concept of graded Jgr-classical 2-absorbing submodule as a generalization of a graded classical 2-absorbing submodule. We give some results concerningof these classes of graded submodules. A proper graded submodule C of M is called a graded Jgr-classical 2-absorbing submodule of M, if whenever rg, sh, ti ∈ h(R) and xj ∈ h(M) with rgshtixj ∈ C, then either rgshxj ∈ C + Jgr(M) or rgtixj ∈ C + Jgr(M) or shtixj ∈ C + Jgr(M), where Jgr(M) is the graded Jacobson radical.

Słowa kluczowe

EN

graded Jgr-classical 2-absorbing submodule; graded classical 2-absorbing submodule; graded 2-absorbing submodule

PL

algebra homologiczna; teoria modułów; podmoduły

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 162--167
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Al-Zoubi Khaldoun

• Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan

autor

Alghueiri Shatha

• Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan

Bibliografia

• [1] K. Al-Zoubi and R. Abu-Dawwas, On graded quasi-prime submodules, Kyungpook Math. J. 55(2015), no. 2, 259-266,DOI: https://doi.org/10.5666/KMJ.2015.55.2.259.
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• [5] K. Al-Zoubi and M. Al-Azaizeh, On graded classical 2-absorbing submodules of graded modules over graded commutativerings, Rend. Istit. Mat. Univ. Trieste 50(2018), 37-46, DOI: https://doi.org/10.13137/2464-8728/20578.
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• [8] K. Al-Zoubi, M. Jaradat, and R. Abu-Dawwas, On graded classical prime and graded prime submodules, Bull. Iranian Math. Soc. 41(2015), no. 1, 217-225.
• [9] K. Al-Zoubi and S. Alghueiri, On graded Jgr-classical prime submodules, submitted.
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• [19] K. Al-Zoubi and A. Al-Qderat, Some properties of graded comultiplication modules, Open Math. 15(2017), 187-192, DOI: https://doi.org/10.1515/math-2017-0016.
• [20] K. Al-Zoubi and S. Alghueiri, On graded Jgr-semiprime submodules, Ital. J. Pure Appl. Math. (to appear).

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).