An embedding theorem for commutative $B_{0}$-algebras

Tracial Algebras and an Embedding Theorem

We prove that every positive trace on a countably generated ∗-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial ∗-algebra can be embedded into a metric ultraproduct of generic matrix algebras. As a particular consequence, every finite von Neumann algebra with separable pre-dual can be embedded into an ultraproduct...

Serre-Swan Theorem for non commutative C∗-algebras

Serre-Swan theorem for non-commutative C∗-algebras. Revised edition

We generalize the Serre-Swan theorem to non-commutative C∗algebras. For a Hilbert C∗-module X over a C∗-algebra A, we introduce a hermitian vector bundle EX associated to X . We show that there is a linear subspace ΓX of the space of all holomorphic sections of EX and a flat connection D on EX with the following properties: (i) ΓX is a Hilbert A-module with the action of A defined by D, (ii) th...

Non-commutative Gröbner Bases for Commutative Algebras

An ideal I in the free associative algebra k〈X1, . . . ,Xn〉 over a field k is shown to have a finite Gröbner basis if the algebra defined by I is commutative; in characteristic 0 and generic coordinates the Gröbner basis may even be constructed by lifting a commutative Gröbner basis and adding commutators.

Commutative pseudo BE-algebras

The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...