(i) | $I_G$ is an D39: Identity element in $G$ |

The

**kernel**of $f$ with respect to $G$ is the D11: Set \begin{equation} \{ x \in X : f(x) = I_G \} \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Enclosed binary operation

▾ Groupoid

▾ Semigroup

▾ Monoid

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Enclosed binary operation

▾ Groupoid

▾ Semigroup

▾ Monoid

Formulation 0

Let $G$ be a D265: Monoid such that

Let $f : X \to G$ be a D18: Map.

The**kernel** of $f$ with respect to $G$ is the D11: Set
\begin{equation}
\{ x \in X : f(x) = I_G \}
\end{equation}

(i) | $I_G$ is an D39: Identity element in $G$ |

The

Also known as

Kernel, Null space

Results