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

 

Hopfian Boolean algebras of power less than or equal to continuum


Author: James T. Loats
Journal: Proc. Amer. Math. Soc. 77 (1979), 186-190
MSC: Primary 06E05
MathSciNet review: 542082
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Abstract: An infinite Boolean algebra (BA) is said to be hopfian if every onto endomorphism is one-to-one. It is shown that there are no countably infinite hopfian BA's. An atomic hopfian BA of power continuum is constructed.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0542082-1
PII: S 0002-9939(1979)0542082-1
Keywords: Hopfian Boolean algebra
Article copyright: © Copyright 1979 American Mathematical Society