Category:Definitions/Maximal Ideals of Rings

From ProofWiki
Jump to navigation Jump to search

This category contains definitions related to Maximal Ideals of Rings.
Related results can be found in Category: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 inclusion.

Pages in category "Definitions/Maximal Ideals of Rings"

The following 3 pages are in this category, out of 3 total.