Idempotent and Regular Elements of the Complete Semigroups of Binary Relations of the Class (original) (raw)

REGULAR ELEMENTS OF THE COMPLETE SEMIGROUPS OF BINARY RELATIONS OF THE CLASS 7 (X, 8)

In this paper let Q = {T1, T2, T3, T4, T5, T6, T7, T8} be a subsemilattice of X−semilattice of unions D where T1 ⊂ T2 ⊂ T3 ⊂ T5 ⊂ T6 ⊂ T8, T1 ⊂ T2 ⊂ T3 ⊂ T5 ⊂ T7 ⊂ T8, T1 ⊂ T2 ⊂ T4 ⊂ T5 ⊂ T6 ⊂ T8, T1 ⊂ T2 ⊂ T4 ⊂ T5 ⊂ T7 ⊂ T8, T1 6= ∅, T4\T3 6= ∅, T3\T4 6= ∅, T6\T7 6= ∅, T7\T6 6= ∅, T3 ∪T4 = T5, T6 ∪T7 = T8, then we characterize the class each element of which is isomorphic to Q by means of the characteristic family of sets, the characteristic mapping and the generate set of Q. Moreover, we calculate the number of regular elements of BX(D) for a finite set X.

Generating Set of the Complete Semigroups of Binary Relations

Difficulties encountered in studying generators of semigroup () X B D 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 () X B D , which are defined by semilattice D, can be generated by the set () () { } X B B D V X D α α * = ∈ = , .