Abstract
Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their investigation problematic. In this work, for special D, it has been seen that the semigroup , which are defined by semilattice D, can be generated by the set .
Highlights
( ) If φ is a mapping of the semilattice D on the family of sets C ( D) which satisfies the condition φ D = P0 and φ ( Zi ) = Pi fo= r any i 1, 2, m −1 and D Z = D \ DT, the following equalities are valid: D = P0 ∪ P1 ∪ P2 ∪ ∪ Pm−1, ( ) Z=i P0 ∪ φ T
It is proved that if the elements of the semilattice D are represented in the form 1, among the parameters
Let α be any binary relation of the semigroup
Summary
( ) If φ is a mapping of the semilattice D on the family of sets C ( D) which satisfies the condition φ D = P0 and φ ( Zi ) = Pi fo= r any i 1, 2, , m −1 and D Z = D \ DT , the following equalities are valid: D = P0 ∪ P1 ∪ P2 ∪ ∪ Pm−1, ( ) Z=i P0 ∪ φ T . (2016) Generating Set of the Complete Semigroups of Binary Relations. Let P0 , P1, P2 , , Pm−1 be parameters in the formal equalities, β ∈ BX ( D) and
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