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On classical n-absorbing submodules
- Source :
- Arabian Journal of Mathematics. 9:425-430
- Publication Year :
- 2019
- Publisher :
- Springer Science and Business Media LLC, 2019.
-
Abstract
- Let R a commutative ring with identity and M be a unitary R-module. In this paper, we investigate some properties of n-absorbing submodules of M as a generalization of 2-absorbing submodules. We also define the classical n-absorbing submodule, a proper submodule N of an R-module M is called a classical n-absorbing submodule if whenever $$a_1 a_2\ldots a_{n+1} m\in N$$ a 1 a 2 … a n + 1 m ∈ N for $$a_1, a_2,\ldots , a_{n+1}\in R$$ a 1 , a 2 , … , a n + 1 ∈ R and $$m \in M$$ m ∈ M , there are n of $$a_i$$ a i ’s whose product with m is in N. Furthermore, we give some characterizations of n-absorbing and classical n-absorbing submodules under some conditions.
Details
- ISSN :
- 21935351 and 21935343
- Volume :
- 9
- Database :
- OpenAIRE
- Journal :
- Arabian Journal of Mathematics
- Accession number :
- edsair.doi...........15658d7d10a2b95e5a4593771afcc174