Generalizations of rad-supplemented modules
Publications de l'Institut Mathematique, cilt.104, sa.118, ss.139-148, 2018 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 104 Sayı: 118
- Basım Tarihi: 2018
- Doi Numarası: 10.2298/pim1818139k
- Dergi Adı: Publications de l'Institut Mathematique
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.139-148
- Anahtar Kelimeler: preradical, Jacobson radical, Rad-supplement, tau-supplement, Communicated by Zoran Petrovic
- İstanbul Gelişim Üniversitesi Adresli: Hayır
Özet
Let R be an associative ring with identity. We introduce the notion of semi-τ-supplemented modules, which is adapted from srs-modules, for a preradical τ on R-Mod. We provide basic properties of these modules. In particular, we study the objects of R-Mod for τ = Rad. We show that the class of semi-τ-supplemented modules is closed under finite sums and factor modules. We prove that, for an idempotent preradical τ on R-Mod, a module M is semi-τ-supplemented if and only if it is τ-supplemented. For τ = 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.