A Class of Balanced Laws on Quasigroups (I)


Branka P. Alimpić




Let $w_1=w_2$ be a balanced law of the I kind [2] in form $$A(u_1,...,u_m)=B(v_1,...,v_n)\;\;m\geq 2,\;\;n\geq 2$$ where $u_i(i=1,...,m)$ is either a variable or a term $A_i(x_{i_1},...,x_{i_\alpha})$, $x_{i_1},...,x_{i_\alpha}$ being variables, analogously $v_j(j=1,...,n)$ is either a variable or a term $B_j(x_{j_1},...,x_{j_\beta})$, $x_{j_1},...,x_{j_\beta}$ being variable. $A,\; B,\; A_i$ and $B_j$ are function letters.