On disjunction of equations in inverse semigroups
Аrtеm N. Shevlyakov · arXiv (Cornell University) · 2013
A semigroup $S$ is an equational domain if any finite union of algebraic sets over $S$ is algebraic. We prove that if an inverse semigroup $S$ is an equational domain in the extended language $\{\cdot,{}^{-1}\}\cup\{s|s\in S\}$ then $S$ is a group.