Definition:Local Ring Homomorphism/Definition 2

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Definition

Let $\struct {A, \mathfrak m}$ and $\struct {B, \mathfrak n}$ be commutative local rings.

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


The homomorphism $f$ is local if and only if the preimage $\map {f^{-1} } {\mathfrak n} \supseteq \mathfrak m$.


Also see


Sources