This article is cited in 6 papers

Rings of quotients of finite $AW^*$-algebras. Representation and algebraic approximation

C. Herrmann^a, M. V. Semenova<sup>bc

a</sup> Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstr. 7, Darmstadt, 64289, Germany
^b Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
^c Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: We show that Berberian's $*$-regular extension of a finite $AW^*$-algebra admits a faithful representation, matching the involution with adjunction, in the $\mathbb C$-algebra of endomorphisms of a closed subspace of some ultrapower of a Hilbert space. It also turns out that this extension is a homomorphic image of a regular subalgebra of an ultraproduct of matrix $*$-algebras $\mathbb C^{n\times n}$.

Keywords: $AW^*$-algebra, finite Rickart $C^*$-algebra, ring of quotients, $*$-regular ring, projection ortholattice, ultraproduct.

UDC: 512.55+512.57

Received: 28.07.2013
Revised: 14.08.2014

 English version: Algebra and Logic, 2014, 53:4, 298–322

Bibliographic databases:

• 
• 
•