\begin{definition}[Definition:Maximal Ideal of Ring/Right]
Let $R$ be a ring.
A right ideal $J$ of $R$ is a '''maximal right ideal''' {{iff}}:
:$(1): \quad J \subsetneq R$
:$(2): \quad$ There is no right ideal $K$ of $R$ such that $J \subsetneq K \subsetneq R$.
Category:Definitions/Maximal Ideals of Rings
\end{definition}