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Algebra Logika, 2014, Volume 53, Number 4, Pages 466–504 (Mi al646)  

This article is cited in 1 scientific paper (total in 1 paper)

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

C. Herrmanna, M. V. Semenovabc

a 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.

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

Bibliographic databases:

UDC: 512.55+512.57
Received: 28.07.2013
Revised: 14.08.2014

Citation: C. Herrmann, M. V. Semenova, “Rings of quotients of finite $AW^*$-algebras. Representation and algebraic approximation”, Algebra Logika, 53:4 (2014), 466–504; Algebra and Logic, 53:4 (2014), 298–322

Citation in format AMSBIB
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\by C.~Herrmann, M.~V.~Semenova
\paper Rings of quotients of finite $AW^*$-algebras. Representation and algebraic approximation
\jour Algebra Logika
\yr 2014
\vol 53
\issue 4
\pages 466--504
\mathnet{http://mi.mathnet.ru/al646}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3309850}
\transl
\jour Algebra and Logic
\yr 2014
\vol 53
\issue 4
\pages 298--322
\crossref{https://doi.org/10.1007/s10469-014-9292-7}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84922073805}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ch. Herrmann, M. Semenova, “Linear representations of regular rings and complemented modular lattices with involution”, Acta Sci. Math., 82:3-4 (2016), 395–442  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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