On quasi n-absorbing submodules
Malik Tusif Ahmed\,^1, Mohammed Issoual\,^2 and Mohammed Tamekkante\,^3
\,^1 Department of Mathematics and Statitscs, Hazara University Mansehra, KPK, Pakistan.
\,^2 CRMEF Fès-Meknès, Morocco.
\,^3 Department of Mathematics, Faculty of Science, Box 11201 Zitoune, University Moulay Ismail Meknes, Morocco.
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Pages 259-267 | Received 20 September 2024, Accepted 20 May 2025, Published 26 January 2026
Abstract
Let R be a commutative ring with 1\neq 0,\ M be an R-module, and n be a positive integer. The purpose of this article is to investigate quasi n-absorbing (resp., weakly quasi n-absorbing) submodules generalizing quasi n-absorbing ideals of rings. We will say a proper submodule N of M is quasi n-absorbing (resp., weakly quasi n-absorbing) submodule of M if whenever a\in R and x\in M with a^{n}x\in N, (resp., 0\neq a^{n}x\in N) then, either a^{n}\in (N:_{R}M) or a^{n-1}x\in N.
Keywords: n-absorbing ideals, n-absorbing submodules, quasi n-absorbing ideals, quasi n-absorbing submodules.
MSC numbers: 13C13, 13A15.
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