Definition 2: An algebraic system is a nonempty set s in which at least one or more operations C1…Q1(k≥1),are defined. We denoted by s; Qis, QkI Z;+] ●[Z;+,2 ]is not an algebraic system• Definition 2: An algebraic system is a nonempty set S in which at least one or more operations Q1 ,…,Qk (k1), are defined. We denoted by [S;Q1 ,…,Qk ]. • [Z;+] • [Z;+,*] • [N;-] is not an algebraic system