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Semiprime submodules of a module and related concepts.
- Source :
-
Journal of Algebra & Its Applications . Aug2019, Vol. 18 Issue 8, pN.PAG-N.PAG. 11p. - Publication Year :
- 2019
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MODULES (Algebra)
*CONCEPTS
*MULTIPLICATION
*NOETHERIAN rings
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 18
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 137326042
- Full Text :
- https://doi.org/10.1142/S0219498819501470