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On the symmetric algebra of quotients of a C*-algebra

Published online by Cambridge University Press:  18 May 2009

Pere Ara
Pere Ara
Affiliation:
Departament de MatemàtiquesUniversitat Autònoma de Barcelona08193 Bellaterra, BarcelonaSpain
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Let R be a semiprime ring (possibly without 1). The symmetric ring of quotients of R is defined as the set of equivalence classes of essentially defined double centralizers (ƒ, g) on R; see [1], [8]. So, by definition, ƒ is a left R-module homomorphism from an essential ideal I of R into R, g is a right R-module homomorphism from an essential ideal J of R into R, and they satisfy the balanced condition ƒ(x)y = xg(y) for x ∈ Iand y ∈ J. This ring was used by Kharchenko in his investigations on the Galois theory of semiprime rings [4] and it is also a useful tool for the study of crossed products of prime rings [7]. We denote the symmetric ring of quotients of a semiprime ring R by Q(R).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 3 , September 1990 , pp. 377 - 379
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

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