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- Title
MODULES THAT HAVE A WEAK RAD-SUPPLEMENT IN EVERY EXTENSION.
- Authors
KIR, EMINE ONAL; CALISICI, HAMZA
- Abstract
As a proper generalization of the modules with the properties (E) and (EE) that were introduced by Zöschinger in terms of supplements, we say that a module M has the property (WRE) (respectively, (WREE)) if M has a weak Rad-supplement (respectively, ample weak Rad-supplements) in every extension. In this paper, we prove that if every submodule of a module M has the property (WRE), then M has the property (WREE). We show that a ring R is semilocal if and only if every left R-module has the property (WRE). Also we prove that over a commutative Von Neumann regular ring a module M has the property (WRE) if and only if M is injective.
- Subjects
MODULES (Algebra); VON Neumann regular rings; POLYNOMIAL rings; FREE algebras; FIELD extensions (Mathematics)
- Publication
Journal of Science & Arts, 2018, Vol 18, Issue 3, p611
- ISSN
1844-9581
- Publication type
Article