Definition:Primary Ideal/Definition 2
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Definition
Let $R$ be a commutative ring with unity.
A proper ideal $\mathfrak q$ of $R$ is called a primary ideal if and only if:
- each zero-divisor of the quotient ring $R / \mathfrak q$ is nilpotent.
Also see
Sources
- 1969: M.F. Atiyah and I.G. MacDonald: Introduction to Commutative Algebra: Chapter $4$: Primary Decomposition