Geodesic
Rings of quotients of finite $AW^*$-algebras. Representation and algebraic approximation
Algebra i logika, Tome 53 (2014) no. 4, pp. 466-504

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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
Mots-clés : ultraproduct. 
@article{AL_2014_53_4_a2,
     author = {C. Herrmann and M. V. Semenova},
     title = {Rings of quotients of finite $AW^*$-algebras. {Representation} and algebraic approximation},
     journal = {Algebra i logika},
     pages = {466--504},
     publisher = {mathdoc},
     volume = {53},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2014_53_4_a2/}
}
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C. Herrmann; M. V. Semenova. Rings of quotients of finite $AW^*$-algebras. Representation and algebraic approximation. Algebra i logika, Tome 53 (2014) no. 4, pp. 466-504. http://geodesic.mathdoc.fr/item/AL_2014_53_4_a2/