Category:Definitions/Kernels of Magma Homomorphisms

This category contains definitions related to Kernels of Magma Homomorphisms.
Related results can be found in Category:Kernels of Magma Homomorphisms.

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 $T$.