Showing papers on "Cancellative semigroup published in 1985"

Ergodic semigroups of epimorphisms

Abstract: The conditions for ergodicity of semigroups of epimorphisms of compact groups are studied. In certain cases ergodic semigroups are shown to contain small ergodic subsemigroups. Properties related to ergodicity, such as that of admitting no infinite closed invariant proper subset of the group, are discussed for semigroups of epimorphisms and of affine transformations.

E-unitaryR-unipotent semigroups

Abstract: By making use of McAlister’s P-theorem [4] O’Carroll proved in [5] that every E-unitary inverse semigroup can be embedded into a semidirect product of a semilattice by a group. Recently an alternative proof of this result was published by Wilkinson [10]. In this paper we generalize this theorem by proving that every E-unitaryR-unipotent semigroup S can be embedded into a semidirect product of a band B by a group where B belongs to the variety of bands generated by the band of idempotents of S.

Left absolutely flat generalized inverse semigroups

Abstract: A semigroup S is called (left, right) absolutely flat if all of its (left, right) S-sets are flat. S is a (left, right) generalized inverse semigroup if S is regula, and its set of idempotents E(S) is a (left, right) normal band (i.e. a strong semilattice of (left zero, right zero) rectangular bands). In this paper it is proved that a generalized inverse semigroup S is left absolutely flat if and only if S is a right generalized inverse semigroup and the (nonidentity) structure maps of E(S) are constant. In particular all inverse semigroups are left (and right) absolutely flat (see (1)). Other consequences are derived.

On the lattice of congruences on an eventually regular semigroup

Abstract: A natural equivalence 6 on the lattice of congruences A(S) of a semigroup S is studied. For any eventually regular semigroup S, it is shown that 0 is a congruence, each 0-class is a complete sublattice of A(S)-and the maximum element in each 0-class is determined.

WE-m semigroups.

Abstract: In this chapter we deal with semigroups in which, for every elements a and b, there is a non-negative integer k such that (ab) m+k =a m b m =(ab) k a m b m , where m is a fixed i n te g er m ≥ 2. These se m igrou p s are c a lled WE- m se m igroups. It is clear that every E-m semigroup is a WE-m semigroup. The examination of WE-m semigroups need some results about E-m semigroups. Thus the E-m semigroups were examined in the previous chapter. As a WE-m semigroup is a left and right Putcha semigroup, it is a semilattice of WE-m archimedean semigroups. We show that the 0-simple WE-mn semigroups are the completely simple E-m semigroups with a zero adjoined. A semigroup is a WE-m archimedean semigroup containing at least one idempotent element if and only if it is a retract extension of a completely simple E-m semigroup by a nil semigroup. We also prove that every WE-2 archimnedean semigroup without idempotent element has a non-trivial group homomorphic image. We deal with the regular WE-m semigroups. We show that the regular WE-m semigroups are exactly the regular exponential semigroups. Moreover, we show that a semigroup which is an ideal extension of a regular semigroup K by a nil sernigroup N is a WE-2 semigroup if and only if K is an E-2 semigroup and the extension is retract. We deal with the subdirectly irreducible WE-2 semigroups.

Constructions of positive commutative semigroups on the plane, II

Abstract: A positive semiroup is a topological semigroup containinq a subseminroup N isomorphic to the multiplicative semigroup of nonnegative real numbers, embedded as