51. 2-ABSORBING AND n-WEAKLY PRIME SUBMODULES.
- Author
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Moradi, S. and Azizi, A.
- Subjects
- *
COMMUTATIVE rings , *PRIME numbers , *PRIME number theorem , *NUMERICAL calculations , *MATHEMATICS - Abstract
Let R be a commutative ring with identity, and let n > 1 be an integer. A proper submodule N of an R-module M will be called 2-absorbing [resp. n-weakly prime], if r; s ∊ R and x ∊M with rsx ∊ N [resp. rsx ∊ N\(N :M)n-1N] implies that rs ∊ (N :M) or rx ∊ N, or sx ∊ N: These concepts are generalizations of the notions of 2-absorbing ideals and weakly prime submodules, which have been studied in [3, 4, 6, 7]. We will study 2-absorbing and n- weakly prime submodules in this paper. Among other results, it is proved that if (N:M)n-1N ≠ (N:M)2N; then N is 2-absorbing if and only if it is n-weakly prime. [ABSTRACT FROM AUTHOR]
- Published
- 2012
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