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- Title
Semiprime submodules of a module and related concepts.
- Authors
Lee, Sang Cheol; Varmazyar, Rezvan
- Abstract
In this paper, we consider the notion of semiprime submodules, which is a natural generation of semiprime ideals. The main purpose of this paper is to give local-global properties of semiprimes and semiprime radicals as well as results on finitely generated multiplication modules. Also, we prove that for every submodule N of a module M , the semiprime radical of N in M is the direct limit of the ascending chain E M (N) ⊆ E M (E M (N)) ⊆ ⋯ of submodules of M , and we prove that N satisfies the semiprime radical formula if and only if its envelope E M (N) in M is semiprime.
- Subjects
MODULES (Algebra); CONCEPTS; MULTIPLICATION; NOETHERIAN rings; ALGEBRA
- Publication
Journal of Algebra & Its Applications, 2019, Vol 18, Issue 8, pN.PAG
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498819501470