Title of article :
ON (n − 1, n)-Φm-PRIME AND (n − 1, n)-WEAKLY PRIME SUBMODULES
Author/Authors :
Ebrahimpour ، M. - Vali-e-Asr University of Rafsanjan , Mirzaee ، F. - Shahid Bahonar University of Kerman
Pages :
11
From page :
99
To page :
109
Abstract :
Let m, n ≥ 2 be two positive integers, R a commutative ring with identity and M a unitary R-module. A proper submodule P of M is an (n − 1, n)-Φm-prime ((n − 1, n)-weakly prime) submodule if a1, . . . , an−1 ∈ R, x ∈ M with a1 . . . an−1x ∈ P \(P : M )m−1P (0 ̸= a1 . . . an 1x ∈ P ) implies a1 . . . a i−1 ai+1 . . . a n−1x ∈ P , for some i ∈ {1, . . . , n − 1} or a1 . . . an−1 ∈ (P : M ). In this paper we study these type of submodules, giving some useful results and examples concerning them.
Keywords :
Quasi , local ring , weakly prime submodule , (n − 1 , n) , weakly prime submodule
Journal title :
Journal of Algebraic Systems
Serial Year :
2018
Journal title :
Journal of Algebraic Systems
Record number :
2452412
Link To Document :
بازگشت