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Trace and the regular ring of a finite $ AW\sp{\ast} $-algebra


Author: S. K. Berberian
Journal: Proc. Amer. Math. Soc. 80 (1980), 584-586
MSC: Primary 46L05; Secondary 16A30, 46L30
DOI: https://doi.org/10.1090/S0002-9939-1980-0587932-6
MathSciNet review: 587932
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Abstract: A finite AW$ ^*$-algebra is of type I if and only if its maximal ring of quotients has a center-valued trace. In particular, a center-valued trace need not be extendible to the maximal (or classical) ring of quotients.


References [Enhancements On Off] (What's this?)

  • [1] S. K. Berberian, The regular ring of a finite $ \mathrm{AW}^*$-algebra, Ann. of Math. (2) 65 (1957), 224-240. MR 0084743 (18:914b)
  • [2] -, Note on a theorem of Fuglede and Putnam, Proc. Amer. Math. Soc. 10 (1959), 175-182. MR 0107826 (21:6548)
  • [3] -, The regular ring of a finite Baer $ \ast $-ring, J. Algebra 23 (1972), 35-65. MR 0308179 (46:7294)
  • [4] -, Baer $ \ast $-rings, Die Grundlehren der math. Wissenschaften, Springer-Verlag, Berlin and New York, 1972.
  • [5] -, Normal derivations in operator algebras, Tôhoku Math. J. (2) 30 (1978), 613-621. MR 516893 (81c:46054)
  • [6] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien (Algèbres de von Neumann), 2nd ed., Gauthier-Villars, Paris, 1969.
  • [7] I. Hafner, The regular ring and the maximal ring of quotients of a finite Baer $ \ast $-ring, Michigan Math. J. 21 (1974), 153-160. MR 0342552 (49:7298)
  • [8] J. Lambek, Lectures on rings and modules, 2nd ed., Chelsea, New York, 1976. MR 0419493 (54:7514)
  • [9] E. S. Pyle, The regular ring and the maximal ring of quotients of a finite Baer $ \ast $-ring, Trans. Amer. Math. Soc. 203 (1975), 201-213. MR 0364338 (51:593)
  • [10] J. E. Roos, Sur l'anneau maximal de fractions des $ \mathrm{AW}^*$-algèbres et des anneaux de Baer, C. R. Acad. Sci. Paris Sér. A 266 (1968), A120-A123.

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DOI: https://doi.org/10.1090/S0002-9939-1980-0587932-6
Article copyright: © Copyright 1980 American Mathematical Society

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