In mathematics, more specifically in ring theory, a maximal ideal is a two-sided ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring R if there are no other two-sided ideals contained between I and R. Maximal ideals are important because the quotients of rings by maximal ideals are simple rings, and in the special case of commutative rings they are also fields.
In mathematics, more specifically in ring theory, a maximal ideal is a two-sided ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring R if there are no other two-sided ideals contained between I and R. Maximal ideals are important because the quotients of rings by maximal ideals are simple rings, and in the special case of commutative rings they are also fields.
Source: Wikipedia "Maximal ideal" · CC BY-SA 4.0
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