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.
Keywords:
introduce notions t rickart strongly t rickart modules provide several characterizations investigate properties each these concepts shown right sigma t extending only every r module t rickart every r module t rickart only oplus prime where prime hereditary right r module examples illustrating results presented
Affiliations des auteurs :
S. Ebrahimi Atani
1
;
M. Khoramdel
1
;
S. Dolati Pish Hesari
1
1
Faculty of Mathematical Sciences University of Guilan P.O. Box 1914, Rasht, Iran
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author = {S. Ebrahimi Atani and M. Khoramdel and S. Dolati Pish Hesari},
title = {T-Rickart modules},
journal = {Colloquium Mathematicum},
pages = {87--100},
year = {2012},
volume = {128},
number = {1},
doi = {10.4064/cm128-1-8},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm128-1-8/}
}
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AU - S. Ebrahimi Atani
AU - M. Khoramdel
AU - S. Dolati Pish Hesari
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S. Ebrahimi Atani; M. Khoramdel; S. Dolati Pish Hesari. T-Rickart modules. Colloquium Mathematicum, Tome 128 (2012) no. 1, pp. 87-100. doi: 10.4064/cm128-1-8
