Abstract
In this paper, we introduce the concepts of $n$-absorbing and strongly $n$-absorbing second submodules as a dual notion of $n$-absorbing submodules of modules over a commutative ring and obtain some related results. In particular, we investigate some results concerning strongly 2-absorbing second submodules.
Highlights
Maleki-Roudposhti abstract: In this paper, we introduce the concepts of n-absorbing and strongly n-absorbing second submodules as a dual notion of n-absorbing submodules of modules over a commutative ring and obtain some related results
The purpose of this paper is to introduce the concepts of n-absorbing and strongly n-absorbing second submodules as dual notion of n-absorbing submodules of modules and provide some information concerning these new classes of modules
We say that N is an n-absorbing second submodule of M if whenever a1...anN ⊆ L for a1, ..., an ∈ R and a completely irreducible submodule L of M, either a1...an ∈ AnnR(N ) or there are n − 1 of ai’s whose their product with N is a subset of L
Summary
We say that N is a strongly n-absorbing second submodule of M if whenever a1...anN ⊆ K for a1, ..., an ∈ R and a submodule K of M , either a1...an ∈ AnnR(N ) or there are n − 1 of ai’s whose their product with N is a subset of K. (a) Let N be a strongly n-absorbing second submodule of M .
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