Homomorphisms and congruences on regular semigroups with associate inverse subsemigroups

An associate inverse subsemigroup of a regular semigroup S is a subsemigroup T of S containing a least associate x* of each x ∈ S, in relation to the natural partial order ≤. In [1] the authors describe the structure of regular semigroups with an associate inverse subsemigroup, satisfying two natural conditions. In this paper we describe all *-homomorphisms and all *-congruences on such semigroups.     

Photolactonisierung: Ein neuer synthetischer Zugang zu Makroliden

Photolactonization: A Novel Synthetic Entry to Macrolides o-Quinol acetates, hydroxyalkylated at C(6), are easily accessible from simple phenols by Wessely acetoxylation (preferentially catalyzed by BF₃). On UV irradiation (in the presence of an appropriate tertiary amine), they are smoothly converted to macrocyclic lactones. Subtle conditions have been elaborated to lead to high overall yields, and the scope of the conversion of phenols to macrolides has been elucidated.     

On one sided and naturally lattice ordered inverse semigroups

We prove that any right amenably and naturally lattice ordered inverse semigroup is already amenably ordered. Among other things this answers a question raised in [6]. August 9, 2000     

The variety of unary semigroups with associate inverse subsemigroup

In Billhardt et al. (Semigroup Forum 79:101–118, 2009) the authors introduced the notion of an associate inverse subsemigroup of a regular semigroup, extending the concept of an associate subgroup of a regular semigroup, first presented in Blyth et al. (Glasg. Math. J. 36:163–171, 1994). The semigroups of these two classes admit axiomatic characterisations in terms of unary operations and can, therefore, be considered as unary semigroups. In this paper we introduce the notion of unary semigroup with associate inverse subsemigroup [with associate subgroup] and show that the classes of such unary semigroups form varieties.     

On inverse semigroups the closure of whose set of idempotents is a clifford semigroup

Communicated by Boris Schein