A new approach to H-supplemented modules via homomorphisms

Hamzekolaee A. R. M., Harmanci A., Talebi Y., ÜNGÖR B.

TURKISH JOURNAL OF MATHEMATICS, cilt.42, sa.4, ss.1941-1955, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 4
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1709-74
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1941-1955
  • Anahtar Kelimeler: H-Supplemented module, E-H-supplemented module, dual Rickart module, small submodule
  • Ankara Üniversitesi Adresli: Evet

Özet

The class of H-supplemented modules, which is a nice generalization of that of lifting modules, has been studied extensively in the last decade. As the concept of homomorphisms plays an important role in module theory, we are interested in H-supplemented modules relative to homomorphisms. Let R be a ring, M a right R-module, and S = End (R)(M) . We say that M is endomorphism H-supplemented (briefly, E - H -supplemented) provided that for every f is an element of S there exists a direct summand D of M such that Imf + X = M if and only if D + X = M for every submodule X of M. In this paper, we deal with the E-H-supplemented property of modules and also a similar property for a module M by considering Hom (R)(N, M) instead of S where N is any module.