Direct sums of ADS* modules


Tribak R., KESKİN TÜTÜNCÜ D., ORHAN ERTAŞ N.

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, cilt.22, ss.33-46, 2016 (ESCI İndekslerine Giren Dergi)

  • Cilt numarası: 22 Konu: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s40590-015-0068-4
  • Dergi Adı: BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA
  • Sayfa Sayısı: ss.33-46

Özet

A module M is called ADS* if for every direct summand N of M and every supplement K of N in M, we have M = N circle plus K. In this work, we study direct sums of ADS* modules. Many examples are provided to show that this notion is not inherited by direct sums. It is shown that if a module M has a decomposition M = A circle plus B which complements direct summands such that A and B are mutually projective, then M is ADS*. The class of rings R, for which all direct sums of ADS* R-modules are ADS*, is shown to be exactly that of the right V-rings. We characterize the class of right perfect rings R for which R circle plus S is ADS* for every simple R-module S as that of the semisimple rings.