We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
ON GENERALIZATIONS OF PRIME SUBMODULES.
- Authors
EBRAHIMPOUR, M.; NEKOOEI, R.
- Abstract
Let R be a commutative ring with identity and M be a unitary R-module. Let ø : S(M) → S(M) ∪ {θ} be a function, where S(M) is the set of submodules of M. Suppose n ⩾ 2 is a positive integer. A proper submodule P of M is called (n - 1, n) - ø-prime, if whenever a1, ... ,an-1 ∊ R and x ∊ M and a1, ... ,an-1x ∊ P\ø(P), then there exists i ∊ {1, ... , n - 1} such that a1, ... ,ai-1ai+1 ... ann-1x ∊ P or a1, ... ,an-1 2 (P : M). In this paper we study (n-1, n)- ø-prime submodules (n ⩾ 2). A number of results concerning (n - 1, n) - ø-prime submodules are given. Modules with the property that for some ø, every proper submodule is (n - 1, n) - ø-prime, are characterized and we show that under some assumptions (n-1, n)-prime submodules and (n-1, n)-øm- prime submodules coincide (n,m ⩾ 2).
- Subjects
MODULES (Algebra); COMMUTATIVE rings; MAXIMAL ideals; PRIME ideals; FACTORIZATION
- Publication
Bulletin of the Iranian Mathematical Society, 2013, Vol 39, Issue 5, p919
- ISSN
1018-6301
- Publication type
Article