T-Rickart Modules And T-dual Rickart Modules

The concepts of t-Rickart modules and t-dual Rickart modules were introduced, and some basic properties were discussed in this article. It is proven that:1. every direct summand of a t-Rickart module (t-dual Rickart module) inherits the prop-erty.2. a module M is a t-Rickart module if and only if M=Z2(M)(?)M’, and M’is a (nonsingular) Rickart moudle;3. a module M is a t-dual Rickart module if and only if Z2(M) is a direct summand of M, and Z2(M) is a dual Rickart module.