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It is well known that the ring radical theory can be approached via languageof modules. In this work, we present some generalizations of classical resultsfrom module theory, in the two-sided sense. We proved that if $\mathsf{M}$ is afinitely generated $\mathsf{G}$-graded $\mathfrak{A}$-bimodule, where$\mathsf{G}$ is an abelian group, $\mathfrak{A}$ is a finite dimensional simple$\mathsf{G}$-graded associative $\mathbb{F}$-algebra, and $\mathbb{F}$ is analgebraically closed field of characteristic zero, then there exist nonzerohomogeneous elements $w_1, w_2,\dots,w_n\in\mathsf{M}$ such that  \begin{equation}\nonumber \mathsf{M}=\mathfrak{A} w_1\oplus\mathfrak{A}w_2\oplus \cdots \oplus \mathfrak{A} w_n \ ,  \end{equation} where $w_i \mathfrak{A}=\mathfrak{A} w_i\neq0$ for all $i=1,2,\dots,n$, and each $\mathfrak{A} w_i$ is irreducible. The elements $w_i$'sare associated to the irreducible characters of $\mathsf{G}$. We also describegraded bimodules over graded semisimple algebras. And we finish by presenting aPierce decomposition of the graded Jacobson radical of any finite dimensional$\mathbb{F}$-algebra with a $\mathsf{G}$-grading.

Irreducible Graded Bimodules over Algebras and a Pierce Decomposition of the Jacobson Radical