Showing papers on "Cancellative semigroup published in 1967"

The Idempotent-separating Congruences on a Regular 0-bisimple Semigroup

Abstract: A congruence ρ on a semigroup is said to be idempotent-separating if each ρ-class contains at most one idempotent. For any idempotent e of a semigroup S the set eSe is a subsemigroup of S with identity e and group of units H e , the maximal subgroup of S containing e . The purpose of the present note is to show that if S is a regular O-bisimple semigroup and e is a non-zero idempotent of 5 then there is a one-to-one correspondence between the idempotentseparating congruences on 5 and the subgroups N of H e with the property that aN ⊆ Na for all right units a of eSe and Nb ⊆ bN for all left units b of eSe. Some special cases of this result are discussed and, in the final section, an application is made to the principal factors of the full transformation semigroup on a set X.

Half-isomorphisms of cancellative semigroups

Abstract: It is proved in this article that every half-isomorphism of a cancellative semigroup onto an arbitrary semigroup is either an isomorphism or an anti-isomorphism.

Topological representation of semigroups

Abstract: This chapter presents a proof that every semigroup S with identity element can be represented by the semigroup Q ( M ) of all quasi-local homeomorphisms of a metric space M into itself. The semigroup Q(M) of all quasi-local homeomorphisms seems to be the most suitable to replace the group of all autohomeomorphisms A(M). The chapter proves the existence of a semigroup S such that there is no Hausdorff-space H such that S is isomorphic to the semigroup of all local homeomorphisms of H into itself. Neither can S be isomorphic to the semigroup of all open continuous mappings of H into itself. f : X → Y is a local homeomorphism if for each x ∈ X there exists an open set O , x ∈ O such that f | O is a homeomorphism of O onto f (0).