$S$ Ideal of $R$ $\,\equiv$$_{\mbox{\scriptsize def}}$$\;\;$$S$ SubGrp of $R$$\downarrow$+gp \& ($\forall$$a$, $b$:$\mid$$R$$\mid$. ($S$($a$)) $\Rightarrow$ ($S$($a$ $\ast$ $b$)))