Definition:Extension of Ideal

From ProofWiki
Jump to navigation Jump to search

This page is about extensions of ideals. For other uses, see Extension.


Let $A$ and $B$ be commutative ring with unity.

Let $f : A \to B$ be a ring homomorphism.

Let $\mathfrak a$ be an ideal of $A$.

The extension of $\mathfrak a$ by $f$ is the ideal generated by its image under $f$:

$\mathfrak a^e = \left\langle f \sqbrk {\mathfrak a} \right\rangle$

Also see