In this paper we give a new proof of the following result of Straubing and Thérien: every J -trivial monoid is a quotient of an ordered monoid satisfying the identity x ≤ 1. We will assume in this paper that the reader has a basic background in finite semigroup theory (in particular, Green’s relations and identities defining varieties) and in computer science (languages, trees, heaps). All semi...

The fundamental concept of a fuzzy set, introduced by Zadeh in his classic paper [5] of 1965, has been applied by many authors to generalize some of the basic notions of algebra. In this note we characterize the semigroups for which each fuzzy ideal is prime, also the semigroups for which each fuzzy right ideal is prime. In Section 2, we prove that a semigroup is fully fuzzy prime if and only i...

There is a well-known combinatorial definition, based on ordered set partitions, of the semigroup of faces of the braid arrangement. We generalize this definition to obtain a semigroup ΣGn associated with G ≀ Sn, the wreath product of the symmetric group Sn with an arbitrary group G. Techniques of Bidigare and Brown are adapted to construct an anti-homomorphism from the Sn-invariant subalgebra ...

We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*algebras as C*-algebras of inverse semigroups, groupoid C*-algebras and full corners in associated group crossed products. These descriptions allow us to characterize nuclear...

We introduce a special set in an implicative semigroup. Using it, an equivalent condition of an ordered filter is stated. We prove that an ordered filter can be represented by the union of such sets. 2000 Mathematics Subject Classification. 20M12, 06F05, 06A06, 06A12.

The most important tool for classifying recognizable languages is Eilenberg’s variety theorem [1], which gives a one-to-one correspondence between (pseudo)-varieties of finite semigroups and varieties of recognizable languages. Varieties of recognizable languages are classes of recognizable languages closed under union, intersection, complement, left and right quotients and inverse morphisms. R...

In this paper we propose a general recipe for calculating the automorphism groups of semigroups consisting of partial endomorphisms of relational structures with a single m-ary relation for any m ∈ N over a finite set. We use this recipe to determine the automorphism groups of the following semigroups: the full transformation semigroup, the partial transformation semigroup, and the symmetric in...