T-dual Rickart modules
نویسندگان
چکیده مقاله:
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.
منابع مشابه
t-dual rickart modules
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 sho...
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عنوان ژورنال
دوره 42 شماره 3
صفحات 611- 642
تاریخ انتشار 2016-06-01
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