Lifting modules with indecomposable decompositions

Er N. F., Ertas N. O.

COMMUNICATIONS IN ALGEBRA, cilt.36, sa.2, ss.395-404, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 2
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1080/00927870701715738
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.395-404
  • Yıldız Teknik Üniversitesi Adresli: Hayır

Özet

A module M is called a "lifting module" if, any submodule A of M contains a direct summand B of M such that A/B is small in M/B. This is a generalization of projective modules over perfect rings as well as the dual of extending modules. It is well known that an extending module with ascending chain condition (a.c.c.) on the annihilators of its elements is a direct sum of indecomposable modules. If and when a lifting module has such a decomposition is not known in general In this article, among other results, we prove that a lifting module M is a direct sum of indecomposable modules if (i) rad(M((I))) is small in M((I)) for every index set I, or, (ii) M has a.c.c. on the annihilators of (certain) elements, and rad(M) is small in M.