We consider various decision problems for automatic semigroups, which involve the provision of an automatic structure as part of the problem instance. With mild restrictions on the automatic structure, which are necessary to make the problem well defined, the uniform word problem for semigroups described by automatic structures is decidable. Under the same conditions, we show that one can also ...

In a recent paper, P.G. Trotter and the author introduced a \regular" semidirect product UV of e-varieties U and V. Among several speciic situations investigated there was the case V = RZ, the e-variety of right zero semigroups. Applying a covering theorem of McAlister, it was shown there that in several important cases (for instance for the e-variety of inverse semigroups), U RZ is precisely t...

We establish a surprisingly close relationship between universal Horn classes of directed graphs and varieties generated by socalled adjacency semigroups which are Rees matrix semigroups over the trivial group with the unary operation of reversion. In particular, the lattice of subvarieties of the variety generated by adjacency semigroups that are regular unary semigroups is essentially the sam...

A semigroup S is said to have the compactness property, or CP for short, if each system of equations over a nite set of variables has an equivalent nite subsystem, that is, having exactly the same solutions in S. We prove that a completely 0-simple semigroup S satis es CP if and only if the group G in a Rees matrix representation S = M0(I; G; ;P) satis es this property. Further, a variety of co...

We establish representation types (finite, tame or wild) of finite dimensional Munn algebras with semisimple bases. As an application, we Rees matrix semigroups, in particular, 0-simple and their mutually annihilating unions.

In this paper we combine results from [1] and [3] in order to determine the relationship between the deficiency of a group G and the deficiency of a Rees matrix semigroup S over G; in particular, we investigate how the efficiency of S depends on the efficiency of G. We start by defining semigroup and group presentations. Let A be an alphabet. We denote by A the free semigroup on A consisting of...

Let I be an ideal of a Noetherian ring R. The Rees algebra of I is the graded R-algebra ⊕k=0Ik. The study of the properties of Rees algebras (and of the other blow-up algebras) has attracted the attention of many researchers in the last three decades. For a detailed account of the theories that have been developed and of the results that have been proved, the reader should consult the monograph...

OF DISSERTATION Tricia Muldoon Brown The Graduate School University of Kentucky 2009 Rees Products of Posets and Inequalities ABSTRACT OF DISSERTATIONOF DISSERTATION A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the College of Arts and Sciences at the University of Kentucky By Tricia Muldoon Brown Lexington, Kentucky Director: Dr. ...

The first collection of a macrofungal agaric species, with morphological features similar to already described Anamika species, has been found in association with animal bones in north Queensland, Australia. This species also shares features with several, commonly occurring and previously described Australian Hebeloma species. An integrated morphological and molecular study has resulted in the ...