On weak Rickart modules


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

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.16, 2017 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 16 Konu: 9
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1142/s0219498817501651
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS

Özet

We introduce and study the notion of w-Rickart modules (i.e. modules M such that for every nonzero endomorphism phi of M, the kernel of phi is contained in a proper direct summand of M). We show that the class of right w-Rickart modules lies properly between the class of right K-nonsingular modules and the class of right Rickart modules. Many properties of w-Rickart modules are established. Some relevant counterexamples are indicated.