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On $ \sp{\ast} $-rings satisfying the square root axiom


Author: Shûichirô Maeda
Journal: Proc. Amer. Math. Soc. 52 (1975), 188-190
MSC: Primary 16A28; Secondary 06A30
DOI: https://doi.org/10.1090/S0002-9939-1975-0371941-4
MathSciNet review: 0371941
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Abstract: It was mentioned by Kaplansky that the parallelogram law is a key property for developing the dimension theory on the lattice of projections of a Baer $ ^{\ast}$-ring, and he proved that this law follows from a pair of axioms: the EP and SR axioms. In this paper, it is shown that this law follows from only the SR axiom.


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

  • [1] S. K. Berberian, Baer $ ^{\ast}$-rings, Die Grundlehren der math. Wissenschaften, Band 195, Springer-Verlag, Berlin and New York, 1972. MR 0429975 (55:2983)
  • [2] S. S. Holland, Jr., Isomorphism between interval sublattices of an orthomodular lattice, Hiroshima Math. J. 3 (1973), 227-241. MR 0340130 (49:4886)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0371941-4
Keywords: Rickart $ ^{\ast}$-ring, Baer $ ^{\ast}$-ring, square root axiom, parallelogram law, lattice of projections
Article copyright: © Copyright 1975 American Mathematical Society

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