This paper introduces the concept of ultimately periodic functions for nite semigroups. Ultimately periodic functions are shown to be the same as regularity-preserving functions in automata theory. This characterization reveals the true algebraic nature of regularity-preserving functions. It makes it possible to prove properties of ultimately periodic functions through automata-theoretic method...

We study inverse semigroup amalgams [S1, S2;U ], where S1 and S2 are finitely presented inverse semigroups with decidable word problem and U is an inverse semigroup with decidable membership problem in S1 and S2. We use a modified version of Bennett’s work on the structure of Schützenberger graphs of the R-classes of S1 ∗U S2 to state sufficient conditions for the amalgamated free products S1 ∗...

In 1996 Jespers and Wang classified finite semigroups whose integral semigroup ring has finitely many units. In a recent paper, Iwaki-Juriaans-Souza Filho continued this line of research by partially classifying the finite semigroups whose rational semigroup algebra contains a Zorder with hyperbolic unit group. In this paper we complete this classification by handling the case in which the semi...

We define two deformations of the Full Transformation Semigroup algebra. One makes the algebra “as semisimple as possible”, while another leads to an eigenvalue result involving Schur functions. Preliminaries The Full Transformation Semigroup on n letters, denoted Tn, is the semigroup of all set maps w : [n] → [n], where [n] = {1, 2, . . . , n} and the multiplication is the usual composition. S...

In this paper it is shown how the graphical methods developed by Stephen for analyzing inverse semigroup presentations may be used to study varieties of inverse semigroups. In particular, these methods may be used to solve the word problem for the free objects in the variety of inverse semigroups generated by the five-element combinatorial Brandt semigroup and in the variety of inverse semigrou...

The representation theory of finite groups began with Frobenius's factorization Dedekind's group determinant. In this paper, we consider the case semigroup determinant is nonzero if and only complex algebra Frobenius, so our results include applications to study Frobenius algebras. We explicitly factor for commutative semigroups inverse semigroups. recover Wilf-Lindström a meet semilattice Wood...

We introduce the notion of the Fourier and Fouier-Stieltjes algebra of a topological ∗-semigroup and show that these are commutative Banach algebras. For a class of foundation semigroups, we show that these are preduals of von Neumann algebras. 1. Definitions and Notations Let S be a locally compact topological semigroup and M(S) be the Banach algebra of all bounded regular Borel measures μ on ...

In this paper we establish that the causal order determined by an Ol’shanski semigroup on the corresponding homogeneous space is globally hyperbolic. Using this fact, we present sufficient conditions for a special class of Lie semigroups to admit a canonical “triple decomposition,” namely those for which the Lie algebra is of Cayley type. This theory applies in particular to semigroups which ar...

We argue that weak containment is an appropriate notion of amenability for inverse semigroups. Given an inverse semigroup S and a homomorphism φ of S onto a group G, we show, under an assumption on ker(φ), that S has weak containment if and only if G is amenable and ker(φ) has weak containment. Using Fell bundle amenability, we find a related result for inverse semigroups with zero. We show tha...

We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse semigroup of finite transformations I n λ of the rank 6 n is algebraically closed in the class of (semi)topological inverse semigroups with continuous inversion. W...