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2017•Zenodo (CERN European Organization for Nuclear Research)Open access

On ϕ - Classes of Submodules

Ashour, Arwa Eid, Mohammed M. Al-Ashker, Al-Hussain Kamal Abu Oda

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Abstract

Let R be a commutative ring with identity and let M be a unitary R-module. Let S(M) be the set of all submodules of M and :S(M)! S(M) S f;g be a function. A proper submodule N of M is said to be a -prime (resp. a -primary) submodule if am 2 N-(N) for a 2 R, m 2 M implies that either m 2 N or a 2 (N : M) (resp. a 2 p (N : M)). These concepts were introduced by N. Zamani and M. Bataineh, in this paper, we study the concept of -primary submodule in details. Also, we introduce the concepts of -primal submodules and -2-absorbing submodules.

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Let R be a commutative ring with identity and let M be a unitary R-module. Let S(M) be the set of all submodules of M and :S(M)! S(M) S f;g be a function. A proper submodule N of M is said to be a -prime (resp. a -primary) submodule if am 2 N-(N) for a 2 R, m 2 M implies that either m 2 N or a 2 (N : M) (resp. a 2 p (N : M)). These concepts were introduced by N. Zamani and M. Bataineh, in this paper, we study the concept of -primary submodule in details. Also, we introduce the concepts of -primal submodules and -2-absorbing submodules.

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Available abstract

Let R be a commutative ring with identity and let M be a unitary R-module. Let S(M) be the set of all submodules of M and :S(M)! S(M) S f;g be a function. A proper submodule N of M is said to be a -prime (resp. a -primary) submodule if am 2 N-(N) for a 2 R, m 2 M implies that either m 2 N or a 2 (N : M) (resp. a 2 p (N : M)). These concepts were introduced by N. Zamani and M. Bataineh, in this paper, we study the concept of -primary submodule in details. Also, we introduce the concepts of -primal submodules and -2-absorbing submodules.

Key concepts: Mathematics, Commutative ring, Unitary state, Identity (music), Prime (order theory), Pure mathematics, Set (abstract data type), Ring (chemistry)

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