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arXiv · 1306.4545

On disjunction of equations in inverse semigroups

Artem N. Shevlyakov
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Abstract

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.

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Artem N. Shevlyakov. 2013-06-19. On disjunction of equations in inverse semigroups. https://arxiv.org/abs/1306.4545

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