maximal ideal
An algebra ideal is called maximal if and if for an ideal then .
Can be thought of that there are no “larger” ideals containing .
Note:
If is maximal, then the quotient is a field with respect to addition and multiplication.
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An algebra ideal I⊂A is called maximal if I=A and if I⊆J⊊A for an ideal J then I=J.
Can be thought of that there are no “larger” ideals containing I.
If I is maximal, then the quotient A/I is a field with respect to addition and multiplication.