ON REGULAR ANTI-CONGRUENCE IN ANTI-ORDERED SEMIGROUPS

Daniel Abraham Romano

Abstract: For an anti-congruence $q$ we say that it is regular anti-congruence on semigroup $(S,=,\neq,\cdot,\alpha)$ ordered under anti-order $\alpha$ if there exists an anti-order $\theta$ on $S/q$ such that the natural epimorphism is a reverse isotone homomorphism of semigroups. Anti-congruence $q$ is regular if there exists a quasi-antiorder $\sigma$ on $S$ under $\alpha$ such that $q=\sigma\cup\sigma^{-1}$. Besides, for regular anti-congruence $q$ on $S$, a construction of the maximal quasi-antiorder relation under $\alpha$ with respect to $q$ is shown.

Keywords: Constructive mathematics, semigroup with apartness, anti-ordered semigroup, anti-congruence, regular anti-congruence, quasi-antiorder

Classification (MSC2000): 03F65; 06F05, 20M10

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