Extensions of Rectangular Band Anti-congruence in Semigroup with Apartness 1
Daniel A. Romano · 2010
The setting of this research is Bishop’s constructive mathematics. Let q be an anticongruence on a semigroup S with apartness. For q we say that it is an rectangular band anticongruence if S/q is a rectangular band. In paper [12] a construction of the maximal rectangular band anticongruence on a semigroup is described. This paper is continuation of that research. Let T be a detachable subsemigroup of a semigroup S. Necessary and sufficient conditions for which any rectangular band anticongruence on T can be extended to rectangular band anticongruence on S are given. Every rectangular band anticongruence on T can be extended to a rectangular band anticongruence on S if and only if the maximal rectangular band anticongruence on T can be extended to a rectangular band anticongruence on S. Mathematics Subject Classification: Primary: 03F65; Secondary 20M10