A set with one or more binary operations gives rise to what is commonly known as a algebraic structure. In particular ,the set of integers under the addition operation '+' is an algebraic structure .It is commonly denoted by (Z,+). In the same way ,the set of rational numbers Q under the usual multiplication operation '*',and denoted by (Q,*),is another algebraic structure .A more complicated algebraic structure is the set of real numbers R together with the two usual operations: addition '+' and multiplication '*' . Such an algebraic structure is denoted by (R,+,*).Algebraic structures with one or more binary operations are given special names depending upon additional properties involved.
An algebraic structure consisting of a set G under an operation * on G, and denoted by(G,*), may enjoy one or more of the following characteristics :
given a,b,c,..... as the elements of the set G, the algebraic structure (G,*) may be