Category:Definitions/Primary Ideals

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This category contains definitions related to Primary Ideals.
Related results can be found in Category:Primary Ideals.


Let $R$ be a commutative ring with unity.


Definition 1

A proper ideal $\mathfrak q$ of $R$ is called a primary ideal if and only if:

$\forall x,y \in R :$
$x y \in \mathfrak q \implies x \in \mathfrak q \; \lor \; \exists n \in \N_{>0} : y^n \in \mathfrak q$


Definition 2

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.

Pages in category "Definitions/Primary Ideals"

The following 3 pages are in this category, out of 3 total.