Definition:Maximal Ideal of Ring/Left
< Definition:Maximal Ideal of Ring(Redirected from Definition:Maximal Left Ideal)
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Definition
Let $R$ be a ring.
A left ideal $J$ of $R$ is a maximal left ideal if and only if:
- $(1): \quad J \subsetneq R$
- $(2): \quad$ There is no left ideal $K$ of $R$ such that $J \subsetneq K \subsetneq R$.