Category:Definitions/Words (Abstract Algebra)

This category contains definitions related to words in the context of abstract algebra.
Related results can be found in Category:Words (Abstract Algebra).

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

Let $S \subseteq M$ be a subset.

A word in $S$ is the product of a finite number of elements of $S$.

The set of words in $S$ is denoted $\map W S$:

$\map W S := \set {s_1 \circ s_2 \circ \cdots \circ s_n: n \in \N_{>0}: s_i \in S, 1 \le i \le n}$