Extensions of Rectangular Band Anti-congruence in Semigroup with Apartness
نویسندگان
چکیده
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
منابع مشابه
A Theorem on Anti - Ordered Factor - Semigroups
Let K be an anti-ideal of a semigroup (S,=, =, ·, θ) with apartness. A construction of the anti-congruence Q(K) and the quasi-antiorder θ, generated by K, are presented. Besides, a construction of the anti-order relation Θ on syntactic semigroup S/Q(K), generated by θ, is given in Bishop’s constructive mathematics.
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