Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06E05

Retrieve articles in all journals with MSC: 06E05

Additional Information

Keywords: Hopfian Boolean algebra
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society