With every E0–semigroup (acting on the algebra of of bounded operators on a separable infinite-dimensional Hilbert space) there is an associated Arveson system. One of the most important results about Arveson systems is that every Arveson system is the one associated with an E0–semigroup. In these notes we give a new proof of this result that is considerably simpler than the existing ones and a...

Sierpiński proved that every countable set of mappings on an infinite set X is contained in a 2-generated subsemigroup of the semigroup of all mappings on X. In this paper we prove that every countable set of endomorphisms of an algebra A which has an infinite basis (independent generating set) is contained in a 2-generated subsemigroup of the semigroup of all endomorphisms of A.

We introduce a notion of covering dimension for Cuntz semigroups C⁎-algebras. This is always bounded by the nuclear C⁎-algebra, and subhomogeneous C⁎-algebras both dimensions agree. Z-stable have at most one. Further, semigroup simple, C⁎-algebra zero-dimensional if only has real rank zero or stably projectionless.

We show that the quantum family of all maps from a finite space to a finite dimensional compact quantum semigroup has a canonical quantum semigroup structure. Let X be a finite space and Y be a compact space. Then the space F (X,Y ) of all maps from X to Y , is a compact space with compact-open topology. The notion of quantum family of all maps, defined by Woronowicz [8] and Soltan [5], is a no...

The setting of this article is Classical algebra and Bishop’s constructive algebra (the algebra based on the Intuitionistic logic). The Esakia’s concept in the classical mathematics of strongly isotone mapping between ordered sets is extended onto two different concepts of mappings: on the concept of weakly isotone and the concept of strongly reverse isotone mapping of relational systems. Some ...

The study of semigroup algebras has a long tradition in commutative algebra. Presentation ideals of semigroup algebras are called toric ideals, in reference to their prominent role in geometry. In this paper we consider the more general class of lattice ideals. Fix a polynomial ring S = k[x1, . . . , xn] over a field k and identify monomials x in S with vectors a ∈ N. Let L be any sublattice of...