A semigroup is a set of elements to which is related an operation usually called multiplication and an equivalence relation, such that the set is closed and associative relative to the operation. We shall discuss, briefly, finite semigroups which are uniquely factorable in the same sense as the multiplicative semigroup of all nonzero integers. Clifford' defined an arithmetic in such a way as to...

We prove that the decision problem of whether or not a finite semigroup has the representation extension property is decidable. 1. The main theorem and preliminaries It is an immediate consequence of the normal form theorem for amalgamated free products of groups that every amalgam of groups embeds in some group. However, this result fails for semigroup amalgams: an early result of Kimura [6] s...

In this paper we introduce and study an algebraic structure, namely Grouplike. A grouplike is something between semigroup and group and its axioms are generalizations of the four group axioms. Every grouplike is a semigroup containing the minimum ideal that is also a maximal subgroup (but the converse is not valid). The first idea of grouplikes comes from b-parts and $b$-addition of real number...

we characterize function spaces of rees matrixsemigroups. then we study these spaces by using the topologicaltensor product technique.

A general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew convolution semigroup. The corresponding affine Markov process is constructed as the strong solution of a system of stochastic equations with non-Lipschitz coefficien...

In this paper we investigate and compare the properties of the semigroup generated by A, and the sequence Ad , n ∈ N, where Ad = (I +A)(I −A)−1. We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger results. If A is the infinitesimal generator of an analytic semigroup, the...

In this paper we investigate the relation between discrete and continuous operators. More precisely, we investigate the properties of the semigroup generated by A, and the sequence Ad , n ∈ N, where Ad = (I +A)(I −A)−1. We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger...

Let E = {E1, . . . , Ek} be a set of regular languages over a finite alphabet Σ. Consider morphism φ : ∆ → (S, ·) where ∆ is the semigroup over a finite set ∆ and (S, ·) = 〈E〉 is the finitely generated semigroup with E as the set of generators and language concatenation as a product. We prove that the membership problem of the semigroup S, the set [u] = {v ∈ ∆ | φ(v) = φ(u)}, is a regular langu...