In this paper we consider the algebra (A, f, g), where f and g are m-ary and n-ary operations on the set A. We define the concept of regular algebra and we prove that for a regular medial algebra (A, f, g) there exists a commutative semigroup (A,+) such that the operations f and g have linear representations on (A,+). As a corollary, we show that for a regular medial algebra (A,F ) there exists...

Inverse semigroups form a variety of unary semigroups, that is, semigroups equipped with an additional unary operation, in this case a 7→ a−1. The theory of inverse semigroups is perhaps the best developed within semigroup theory, and relies on two factors: an inverse semigroup S is regular, and has semilattice of idempotents. Three major approaches to the structure of inverse semigroups have e...

in this paper we find sufficient conditions on primitive inverse topological semigroup s under which: the inversion inv : (h(s)) (h(s)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed h-classes is topologically isomorphic to an orthogonal sum p i2= bi (gi) of topological brandt extensions bi (gi) of countably compac...

In the present paper, we consider biflatness of certain classes of semigroupalgebras. Indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. Also, for a certain class of inversesemigroups S, we show that the biflatness of ell^{1}(S)^{primeprime} is equivalent to the biprojectivity of ell^{1}(S).

This paper addresses extensions of the complex Ornstein-Uhlenbeck semigroup to operator algebras in free probability theory. If a1, . . . , ak are ∗-free R-diagonal operators in a II1 factor, then Dt(ai1 · · · ain) = e −ntai1 · · · ain defines a dilation semigroup on the non-self-adjoint operator algebra generated by a1, . . . , ak. We show that Dt extends (in two different ways) to a semigroup...

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 ...

It is known [l; 2] that every inverse semigroup 5 has a faithful representation as a semigroup of (1, l)-mappings of subsets of a set A into A. The set A may be taken as the set of elements of 5 and the (1, l)-mappings as mappings of principal left ideals of 5 onto principal left ideals of 5. If £ is the set of idempotents of 5 then there is also a representation of 5, not necessarily faithful,...

Associative and commutative algebras with identity have various well-known applications. In particular, many classical codes are ideals in commutative algebras (see [4], [12] for references). Computer storage, encoding and decoding algorithms simplify if all these codes have single generator polynomials. Thus it is of interest to determine when all ideals of an algebra are principal. In [5] Dec...

This paper is a survey of recent results in the theory of nite semigroups using syntactic techniques. This involves manipulating pseudoidentities and the study of relatively free proonite semigroups, whose structure encodes algebraic and combinatorial properties common to the members of a pseudovariety of semigroups. These techniques are illustrated with applications in the study of semigroups ...