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 (respectively, finitely generated free) R-module is T-dual Rickart if and only if (Z) over bar (2) (R) is a direct summand of R and End((Z) over bar (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. Examples illustrating the results are presented.