Module decompositions via Rickart modules

Harmanci A., ÜNGÖR B.

ALGEBRA & DISCRETE MATHEMATICS, cilt.26, sa.1, ss.47-64, 2018 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Sayı: 1
  • Basım Tarihi: 2018
  • Dergi Adı: ALGEBRA & DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.47-64
  • Anahtar Kelimeler: Soc(.)-inverse split module, Rad(.)-inverse split module, Rickart module, RINGS
  • Ankara Üniversitesi Adresli: Evet

Özet

This work is devoted to the investigation of module decompositions which arise from Rickart modules, socle and radical of modules. In this regard, the structure and several illustrative examples of inverse split modules relative to the socle and radical are given. It is shown that a module M has decompositions M = Soc(M) circle plus N and M = Rad(M) circle plus K where N and K are Rickart if and only if M is Soc(M)-inverse split and Rad(M)-inverse split, respectively. Right Soc(.)-inverse split left perfect rings and semiprimitive right hereditary rings are determined exactly. Also, some characterizations for a ring R which has a decomposition R = Soc(R-R) circle plus I with I a hereditary Rickart module are obtained.