T-Rickart modules
Volume 128 / 2012
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.
