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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0371941-4
PII: S 0002-9939(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