Abstract:

Let Λ be an arbitrary nonempty set, and Γ be a semilattice on the set Λ, semigroup PΓ(Λ×Λ) is a semigroup of binary relations determined by the semilattice Γ on the set Λ. Use of the nature of the semilattice,characteristics of idempotents of the semigroup PΓ(Λ×Λ) are obtained,and a class of idempotents is constructed; Finally, left units of the semigroup PΓ(Λ×Λ) are characterized.

Key words:  semigroup of binary relations; idempotents; left units