Finitely generated ideal

Definition for commutative rings

Symbol-free definition

An ideal in a commutative unital ring is said to be finitely generated if it has a finite generating set, that is, if there is a finite set such that it is the smallest ideal containing that finite set.

Definition with symbols

An ideal $I$ in a commutative unital ring $R$ is said to be finitely generated if there is a finite set $x_1,x_2,...,x_n$ such that $I=R{x}_1+R{x}_2+...+R{x}_n$.

Definition for noncommutative rings

Symbol-free definition

An ideal in a commutative unital ring is said to be finitely generated if it has a finite generating set, that is, if there is a finite set such that it is the smallest ideal containing that finite set.

Definition with symbols

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