Relations between G-part and Atoms in Q-algebras

In this work the concepts of $G$-part $G(X)$, atoms and strong atoms in $Q$-algebras are discussed. We provide some connections among $G(X)$, set of all atoms and set of all strong atom of $X$ which related to the concept of ideal. We prove that a $Q$-algebra $X$ does not contain a strong atom whenever it contains a non-zero ideal $G(X)$. In addition, we provide some conditions that make a set of all atom is an abelian group.