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Generalizations of Rad-Supplemented Modules
- Publication Year :
- 2018
- Publisher :
- Publications L Institut Mathematique Matematicki, 2018.
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Abstract
- WOS: 000446696800011 Let R be an associative ring with identity. We introduce the notion of semi-tau-supplemented modules, which is adapted from srs-modules, for a preradical tau on R-Mod. We provide basic properties of these modules. In particular, we study the objects of R-Mod for tau = Rad. We show that the class of semi-tau-supplemented modules is closed under finite sums and factor modules. We prove that, for an idempotent preradical tau on R-Mod, a module M is semi-tau-supplemented if and only if it is tau-supplemented. For tau = Rad, over a local ring every left module is semi-Rad-supplemented. We also prove that a commutative semilocal ring whose semi-Rad-supplemented modules are a direct sum of w-local left modules is an artinian principal ideal ring. Amasya UniversityAmasya University [FMB-BAP 15-107] The authors sincerely thank Engin Buyukasik for his interest and helpful suggestions. Supported by Scientific Research Project in Amasya University FMB-BAP 15-107.
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....f0dfa1e4e9dfc971c367975231d03101