Two classes of linear involutory semigroups We construct two classes of involutory semigroups, which together with two already known generating rules yield n linear involutory semigroups of order n, where 2n = 2 n+2 ? 1 2 (n + 1)(n + 6) ; 2n+1 = 3 2 n+1 ? 1 2 (n 2 + 9n + 10) (1) for n 1. By the way, we extend the rule for the construction of linear archimedian involutory semigroups in L. Berg a...

This paper deals with semihyperbolic semigroups which are generated by entire (possibly transcendental) functions. In particular, a criterion is given assuring that a given entire semigroup is semihyperbolic. Note that a semihyperbolic semigroup G admit holomorphic scaling, that is to say, the branches of local inverses of functions f 2 G are of bounded degree and that the preimages shrink to z...

This paper explores the following regularity properties and their relationships for simple, not-necessarily-unital C∗algebras: (i) Jiang-Su stability, (ii) unperforation in the Cuntz semigroup, and (iii) slow dimension growth (applying only in the case that the C∗-algebra is approximately subhomogeneous). An example is given of a simple, separable, nuclear, stably projectionless C∗-algebra whos...

The intersection of all two-sided ideals of an ordered semigroup, if it is non-empty, is called the kernel of the ordered semigroup. A left ideal L of an ordered semigroup (S, ·,≤) having a kernel I is said to be simple if I is properly contained in L and for any left ideal L′ of (S, ·,≤), I is properly contained in L′ and L′ is contained in L imply L′ = L. The notions of simple right and two-s...

A semigroup whose bi-ideals and quasi-ideals coincide is called a -semigroup. The full transformation semigroup on a set X and the semigroup of all linear transformations of a vector space V over a field F into itself are denoted, respectively, by T(X) and LF(V). It is known that every regular semigroup is a -semigroup. Then both T(X) and LF(V) are -semigroups. In 1966, Magill introduced and st...

Let A be a semigroup whose only invertible element is 0. For an A-homogeneous ideal we discuss the notions of simple i-syzygies and simple minimal free resolutions of R/I. When I is a lattice ideal, the simple 0-syzygies of R/I are the binomials in I. We show that for an appropriate choice of bases every A-homogeneous minimal free resolution of R/I is simple. We introduce the gcd-complex ∆gcd(b...

Employing the construction method of Dirichlet forms on standard forms of von Neu-mann algebras developed in Pa], we construct Dirichlet forms and associated symmetric Markovian semigroups on CCR algebras with respect to quasi-free states. More precisely, let A(h 0) be the CCR algebra over a complex separable pre-Hilbert space h 0 and let ! be a quasi-free state on A(h 0). For any normalized ad...

Let E be a real Banach space. We study the Ornstein-Uhlenbeck semigroup P = {P (t)}t≥0 associated with the Ornstein-Uhlenbeck operator Lf(x) = 1 2 TrQDf(x) + 〈Ax,Df(x)〉, x ∈ E. Here Q ∈ L (E, E) is a positive symmetric operator and A is the generator of a C0-semigroup S = {S(t)}t≥0 on E. Under the assumption that P admits an invariant measure μ∞ we prove that if S is eventually compact and the ...