Modules in Which Inverse Images of Some Submodules are Direct Summands

ÜNGÖR B., HALICIOĞLU S., Harmanci A.

COMMUNICATIONS IN ALGEBRA, cilt.44, sa.4, ss.1496-1513, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 4
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1080/00927872.2015.1027355
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1496-1513
  • Anahtar Kelimeler: F-inverse split module, Rickart module, T-Rickart module, RICKART MODULES, RINGS
  • Ankara Üniversitesi Adresli: Evet

Özet

Let R be an arbitrary ring with identity and M a right R-module with S=End(R)(M). Let F be a fully invariant submodule of M. We call M an F-inverse split module if f(-1)(F) is a direct summand of M for every fS. This work is devoted to investigation of various properties and characterizations of an F-inverse split module M and to show, among others, the following results: (1) the module M is F-inverse split if and only if M=F circle plus K where K is a Rickart module; (2) for every free R-module M, there exists a fully invariant submodule F of M such that M is F-inverse split if and only if for every projective R-module M, there exists a fully invariant submodule F of M such that M is F-inverse split; and (3) Every R-module M is Z(2)(M)-inverse split and Z(2)(M) is projective if and only if R is semisimple.