The five-element Brandt semigroup B2 and its four-element subsemigroup B0, obtained by omitting one nonidempotent, have played key roles in the study of varieties of semigroups. Regarded in that fashion, they have long been known to be finitely based. The semigroup B2 carries the natural structure of an inverse semigroup. Regarded as such, in the signature {·,−1 }, it is also finitely based. It...

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...

We give an embedding of a quotient of the Witt semigroup into the lattice of rational cellular classes represented by formal 2-cones between S2n and the two-cell complex Xn = S2n ∪[ι,ι] e4n (n ≥ 1).

A totally ordered monoid, or tomonoid for short, is a monoid endowed with a compatible total order. We deal in this paper with tomonoids that are finite and negative, where negativity means that the monoidal identity is the top element. Examples can be found, for instance, in the context of finite-valued fuzzy logic. By a Rees coextension of a negative tomonoid S, we mean a negative tomonoid T ...

Neretin and Segal independently defined a semigroup of annuli with boundary parametrizations, which is viewed as a complexification of the group of diffeomorphisms of the circle. By extending the parametrizations to quasisymmetries, we show that this semigroup is a quotient of the Teichmüller space of doubly-connected Riemann surfaces by a Z action. Furthermore, the semigroup can be given a com...

This thesis studies subsemigroups of groups from three perspectives: automatic structures, ordinary semigroup presentations, and Malcev presentaions. [A Malcev presentation is a presentation of a special type for a semigroup that can be embedded into a group. A group-embeddable semigroup is Malcev coherent if all of its finitely generated subsemigroups admit finite Malcev presentations.] The th...

We study various complexity properties of suffix-free regular languages. The quotient complexity of a regular language L is the number of left quotients of L; this is the same as the state complexity of L, which is the number of states in a minimal deterministic finite automaton (DFA) accepting L. A regular language L′ is a dialect of a regular language L if it differs only slightly from L (for...

We study congruences on the partial automorphism monoid of a finite rank free group action. determine decomposition congruence this into Rees congruence, Brandt semigroup and an idempotent separating congruence. The constituent parts are further described in terms subgroups direct semidirect products groups. utilize description to demonstrate how number depends

An M-polysymmetrical hyperring $(R,+,cdot )$ is an algebraic system, where $(R,+)$ is an M-polysymmetrical hypergroup, $(R,cdot )$ is a semigroup and $cdot$ is bilaterally distributive over $+$. In this paper, we introduce the concept of hyperideals of an M-polysymmetrical hyperring and by using this concept, we construct an ordinary quotient ring. Finally, the fundamental theorem of homomorphi...

Let T{t) be a Co-semigroup of linear operators on a Banach space X, and let X® , resp. X® , denote the closed subspaces of X" consisting of all functionals x* such that the map t •-» T*{t)x* is strongly continuous for t > 0, resp. t > 0. Theorem. Every nonzero orbit of the quotient semigroup on X*/X® is nonseparably valued. In particular, orbits in X*/X® are either zero for t > 0 or nonseparabl...