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Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module with$S=$ End$_R(M)$. Let $Z_2(M)$ be the second singular submodule of $M$. In thispaper, we define Goldie Rickart modules by utilizing the endomorphisms of amodule. The module $M$ is called Goldie Rickart if for any $f\in S$,$f^{-1}(Z_2(M))$ is a direct summand of $M$. We provide severalcharacterizations of Goldie Rickart modules and study their properties. Also wepresent that semisimple rings and right $\Sigma$-$t$-extending rings admit somecharacterizations in terms of Goldie Rickart modules.

Rickart Modules Relative to Goldie Torsion Theory