A generalization of supplemented modules

Inankil H., HALICIOĞLU S., Harmanci A.

ALGEBRA & DISCRETE MATHEMATICS, cilt.11, sa.1, ss.59-74, 2011 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 1
  • Basım Tarihi: 2011
  • Dergi Adı: ALGEBRA & DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.59-74
  • Anahtar Kelimeler: supplemented modules, delta-supplemented modules, principally delta-supplemented modules, semiperfect modules, delta-semiperfect modules, principally delta-semiperfect modules
  • Ankara Üniversitesi Adresli: Evet

Özet

Let R be an arbitrary with identity and I a right R-module. In this paper, we introduce a class of modules which is an analogous of delta-supplemented modules defined by Kosan. The module is called principally delta-supplemented, for all m E there exists a submodule A of M with M = mR + A and (mR) boolean AND A delta-small in A. We prove that sonic results of delta-supplemented modules can be extended to principally delta-supplemented modules for this general settings. We supply some examples showing that there are principally delta-supplemented modules but riot delta-supplemented. We also introduce principally delta-semiperfect modules as a generalization of a-semiperfect modules and investigate their properties.