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- Title
Closure of Minimal Extensions.
- Authors
El Hajoui, M.; Miri, A.
- Abstract
Let R be a commutative ring with a unit and M an R-module. In this paper we give a comparison between the F-closure in M of an R-submodule having a minimal extension and the closure of this minimal extension for the same Gabriel topology defined on the ring R. If J(R) ∈ F we prove that both closures are the same. Moreover, if R is Artinian or semi-simple then the converse also holds.
- Subjects
RING extensions (Algebra); COMMUTATIVE rings; MODULES (Algebra); TOPOLOGICAL rings; RING theory
- Publication
Turkish Journal of Mathematics, 2007, Vol 31, Issue 4, p409
- ISSN
1300-0098
- Publication type
Article