Communications of the
Korean Mathematical Society CKMS

In this paper, we show that the mapping $\varphi(x)=0*x$ is an endomorphism of a $Q$-algebra $X$, which induces a congruence relation ``$\ \sim \ $" such that $X/{\varphi}$ is a medial $Q$-algebra. We also study some decompositions of ideals in $Q$-algebras and obtain equivalent conditions for closed ideals. Moreover, we show that if $I$ is an ideal of a $Q$-algebra $X$, then $I^g$ is an ignorable ideal of $X$.

Keywords: $Q$-algebra, medial $Q$-algebra

MSC numbers: 06F35, 03G25