Category:Maximal Ideals of Rings

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This category contains results about Maximal Ideals of Rings.
Definitions specific to this category can be found in Definitions/Maximal Ideals of Rings.

Let $R$ be a ring.

An ideal $J$ of $R$ is maximal if and only if:

$(1): \quad J \subsetneq R$
$(2): \quad$ There is no ideal $K$ of $R$ such that $J \subsetneq K \subsetneq R$.

That is, if and only if $J$ is a maximal element of the set of all proper ideals of $R$ ordered by the subset relation.