A subset I of a ring R is an ideal if it is closed under multiplication by all elements of R
Ideal generated by 1 element
Ideal that does not contain units
An ideal that does not contain the entire ring and is only contained by the ring and itself
An ideal P where ab in P requires a or b be in P
If A is a nonempty partially ordered set in which every chain has an upper bound, A has a maximal element
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