T-Rickart modules

Volume 128 / 2012

S. Ebrahimi Atani, M. Khoramdel, S. Dolati Pish Hesari Colloquium Mathematicum 128 (2012), 87-100 MSC: Primary 05C40, 05C45; Secondary 16P10. DOI: 10.4064/cm128-1-8

Abstract

We introduce the notions of T-Rickart and strongly T-Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that $R$ is right $\Sigma $-t-extending if and only if every $R$-module is T-Rickart. Also, every free $R$-module is T-Rickart if and only if $R=Z_2(R_R)\oplus R^\prime $, where $R^\prime $ is a hereditary right $R$-module. Examples illustrating the results are presented.

Authors

  • S. Ebrahimi AtaniFaculty of Mathematical Sciences
    University of Guilan
    P.O. Box 1914, Rasht, Iran
    e-mail
  • M. KhoramdelFaculty of Mathematical Sciences
    University of Guilan
    P.O. Box 1914, Rasht, Iran
    e-mail
  • S. Dolati Pish HesariFaculty of Mathematical Sciences
    University of Guilan
    P.O. Box 1914, Rasht, Iran
    e-mail

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