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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
DOI: https://doi.org/10.1090/S0002-9939-1979-0542082-1
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.


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

  • [1] J. Loats and M. Rubin, Boolean algebras without nontrivial onto endomorphisms exist in every uncountable cardinality, Proc. Amer. Math. Soc. 72 (1978), 346-351. MR 507336 (80f:03071)
  • [2] D. Martin and M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), 143-178. MR 42 #5787. MR 0270904 (42:5787)
  • [3] R. McKenzie and J. D. Monk, On automorphism groups of Boolean algebras, Colloq. Math. Publ. 10 (1973), 951-988. MR 51 #12651. MR 0376476 (51:12651)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0542082-1
Keywords: Hopfian Boolean algebra
Article copyright: © Copyright 1979 American Mathematical Society

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