SIFAT-SIFAT RING FAKTOR YANG DILENGKAPI DERIVASI

Abstract

Let $R$ is a ring with unit element and $\delta$ is a derivation on $R$. An ideal $I$ of $R$ is called $\delta$-ideal if it satisfies $\delta (I)\subseteq I$. Related to the theory of ideal, we can define prime $\delta$-ideal and maximal $\delta$-ideal. The ring $R$ is called $\delta$-simple if $R$ is non-zero and the only $\delta$-ideal of $R$ are ${0}$ and $R$. In this paper, given the necessary and sufficient conditions for quotient ring $R/I$ is a $\delta$-simple where $\delta_*$ is a derivation on $R/I$ such that $\delta_* \circ \pi =\pi \circ \delta$.