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

 

A Schröder-Bernstein theorem in Baer$ \sp{\ast}$-rings with lattice-theoretic proof


Author: Jôsuke Hakeda
Journal: Proc. Amer. Math. Soc. 76 (1979), 131-132
MSC: Primary 06A23; Secondary 16A28
MathSciNet review: 534403
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Abstract: The Schröder-Bernstein theorem (SB-theorem) for $ *$-equivalence of projections of a $ \mathrm{Baer}^*$-ring is known.

Here, we will prove an SB-theorem for algebraic equivalence (Theorem A) as a consequence of a lattice-theoretic SB-theorem (Theorem B). Theorem A and the known result about $ *$-equivalence will be derived from Theorem B.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0534403-0
PII: S 0002-9939(1979)0534403-0
Keywords: Schröder-Bernstein theorem, Baer$ ^*$-ring, orthomodular lattice, complete lattice
Article copyright: © Copyright 1979 American Mathematical Society