Category:Local Ring Homomorphisms
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This category contains results about Local Ring Homomorphisms.
Definitions specific to this category can be found in Definitions/Local Ring Homomorphisms.
Let $\struct {A, \mathfrak m}$ and $\struct {B, \mathfrak n}$ be commutative local rings.
Let $f : A \to B$ be a unital ring homomorphism.
Definition 1
The homomorphism $f$ is local if and only if the image $f(\mathfrak m) \subseteq \mathfrak n$.
Definition 2
The homomorphism $f$ is local if and only if the preimage $\map {f^{-1} } {\mathfrak n} \supseteq \mathfrak m$.
Definition 3
The homomorphism $f$ is local if and only if the preimage $\map {f^{-1} } {\mathfrak n} = \mathfrak m$.
Pages in category "Local Ring Homomorphisms"
This category contains only the following page.