Definition:Kernel of Magma Homomorphism

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This page is about Kernel of Magma Homomorphism. For other uses, see Kernel.

Definition

Let $\struct {S, \circ}$ be a magma.

Let $\struct {T, *}$ be an algebraic structure with an identity element $e$.

Let $\phi: \struct {S, \circ} \to \struct {T, *}$ be a homomorphism.


The kernel of $\phi$ is the subset of the domain of $\phi$ defined as:

$\map \ker \phi = \set {x \in S: \map \phi x = e}$


That is, $\map \ker \phi$ is the subset of $S$ that maps to the identity of $T$.