In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for theâ€¦ (More)

w x T. E. Hall proved in 1978 that if S , S ; U is an amalgam of regular semigroups 1 2 Å½ in which S l S s U is a full regular subsemigroup of S and S i.e., S , S , and 1 2 1 2 1 2 . U have the sameâ€¦ (More)

We compute the quiver of any finite monoid that has a basic algebra over an algebraically closed field of characteristic zero. More generally, we reduce the computation of the quiver over a splittingâ€¦ (More)

We prove that the pseudovarieties of all finite semigroups, and of all aperiodic fin1 e sernigroups are irreducible for join, for semidirect product and for hlal 'ce~. product. In particular, theseâ€¦ (More)

The subword relation reveals interesting combinatorial properties and plays a prominent role in formal language theory. For instance, recall that languages consisting of all words over Î£ having aâ€¦ (More)

We develop the homology theory of the algebra of a regular semigroup, which is a particularly nice case of a quasi-hereditary algebra in good characteristic. Directedness is characterized for theseâ€¦ (More)

INTRODUCTION
The unequal and inequitable distribution of the medical workforce between rural and urban parts of Australia has been well documented. Commonwealth and state governments have introducedâ€¦ (More)