T-dual Rickart modules

Authors

M. Khoramdel Department of‎ ‎Mathematics, University‎ ‎of Guilan‎, ‎P.O. Box 1914, Rasht‎, ‎Iran.

S. Dolati Pish Hesari Department of Mathematics, ‎University‎ ‎of Guilan‎, ‎P.O. Box 1914, Rasht‎, ‎Iran.

S. Ebrahimi Atani Department of Mathematics, University‎ ‎of Guilan‎, ‎P.O. Box 1914, Rasht‎, ‎Iran.

Abstract:

We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) $R$-module is T-dual Rickart if and only if $overline{Z}^2(R)$ is a direct summand of $R$ and End$(overline{Z}^2(R))$ is a semisimple (resp. regular) ring. It is shown that, while a direct summand of a (strongly) T-dual Rickart module inherits the property, direct sums of T-dual Rickart modules do not. Moreover, when a direct sum of T-dual Rickart modules is T-dual Rickart, is included. Examplesillustrating the results are presented.

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Journal title

Bulletin of the Iranian Mathematical Society

volume 42 issue 3

pages 611- 642

publication date 2016-06-01

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Keywords

Dual Rickart modules t-lifting modules t-dual Baer modules T-dual Rickart modules strongly T-dual Rickart modules

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