In this paper we answer a question raised in [Mol] by giving an example of a proper standard C∗-subalgebra of B(H) whose automorphism and isometry groups are topologically reflexive. After this we prove that in the case of extensions of the C∗-algebra C(H) of all compact operators by separable commutative C∗algebras, these groups are algebraically reflexive. Concerning the most well-known exten...

In his classic book, Modern Algebra, van der Waerden gave a procedure for factoring polynomials over a …nite-dimensional, separable, simple extension …eld. I believe that there is a nonconstructive component to his proof, and I will indicate where it comes in and why. Although I’m sure that this component could be avoided while staying within the framework that he set down, it is simpler to get...

According to J. Feldman and C. Moore's well-known theorem on Cartan subalgebras, a variant of the group measure space construction gives an equivalence of categories between twisted countable standard measured equivalence relations and Cartan pairs, i.e. a von Neumann algebra (on a separable Hilbert space) together with a Cartan subalgebra. A. Kumjian gave a C *-algebraic analogue of this theor...

We introduce a framework within which reasoning according to à Lukasiewicz logic can be represented. We consider a separable Boolean algebra B endowed with a (certain type of) group G of automorphisms; the pair (B, G) will be called a Boolean ambiguity algebra. B is meant to model a system of crisp properties; G is meant to express uncertainty about these properties. We define fuzzy proposition...

We formally introduce the concept of localizing the Elliott conjecture at a given strongly self-absorbing C∗-algebra D; we also explain how the known classification theorems for nuclear C∗-algebras fit into this concept. As a new result in this direction, we show that the class of separable, unital, simple C∗-algebras with locally finite decomposition rank and UCT, and for which projections sep...

The model theory of metric structures ([?]) was successfully applied to analyze ultrapowers of C*-algebras in [?] and [?]. Since important classes of separable C*-algebras, such as UHF, AF, or nuclear algebras, are not elementary (i.e., not characterized by their theory—see [?, §6.1]), for a moment it seemed that model theoretic methods do not apply to these classes of C*-algebras. We prove res...

We prove that every place P of an algebraic function field F |K of arbitrary characteristic admits local uniformization in a finite extension F of F . We show that F|F can be chosen to be Galois, after a finite purely inseparable extension of the ground field K. Instead of being Galois, the extension can also be chosen such that the induced extension FP |FP of the residue fields is purely insep...

Abstract Let R be a discrete valuation domain with field of fractions Q and maximal ideal generated by $\pi $ . $\Lambda an -order such that $Q\Lambda is separable -algebra. Maranda showed there exists $k\in \mathbb {N}$ for all -lattices L M , if $L/L\pi ^k\simeq M/M\pi ^k$ then $L\simeq M$ Moreover, complete indecomposable -lattice, also indecomposable. We extend Maranda’s theorem to the clas...

Starting from Kirchberg’s theorems announced at the operator algebra conference in Genève in 1994, namely O2 ⊗A ∼= O2 for separable unital nuclear simple A and O∞ ⊗A ∼= A for separable unital nuclear purely infinite simple A, we prove that KK-equivalence implies isomorphism for nonunital separable nuclear purely infinite simple C∗-algebras. It follows that if A and B are unital separable nuclea...