Definition:Algebraic Structure

An algebraic structure is a set $$S$$ which has one or more binary operations $$\circ_1, \circ_2, \ldots, \circ_n$$ defined on all the elements of $$S \times S$$, and is denoted $$\left({S, \circ_1, \circ_2, \ldots, \circ_n}\right)$$.

$$\left({S, \circ}\right)$$ or $$\left({T, *}\right)$$, etc. are the symbols usually used for the general algebraic structure with one (binary) operation.

The underlying set of the algebraic structure $$\left({S, \circ}\right)$$ is the set $$S$$.

Two algebraic structures $$\left({S, \circ}\right)$$ and $$\left({T, *}\right)$$ are equal iff:


 * $$S = T$$
 * $$\forall a, b \in S: a \circ b = a * b$$