Showing papers on "Bicyclic semigroup published in 1967"

Automorphisms of the semigroup of all differentiable functions

Abstract: Let R denote the space of real numbers and let D(R) denote the family of all functions mapping R into R that are (finitely) differentiable at each point of R. Since the composition f o g of two differentiable functions is also differentiable and since the composition operation is associative, it follows that D(R) is a semigroup with this operation. Such semigroups have been studied previously. Nadler, in [4], has shown that the semigroup of al differentiable functions mapping the closed unit interval into itself has no idempotent elements other than the identity function and the constant functions. The proof of that result carries over easily to the semigroup D(R).

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).