On equations in inverse semigroups

Abstract.

Let S be an inverse semigroup generated by a set $A = \{{a_j | j \in J}\}$. An equation in S is an expression $w (x_1,\ldots,x_n) = w'(x_1,\ldots,x_n), \textrm{where}\quad w(x_1,\ldots,x_n)\quad\textrm{and}\quad w'(x_1,\ldots,x_n)$, are terms of the type $\{\cdot,^{-1}\}\bigcup A$.