Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Boolean algebras with no rigid or homogeneous factors
HTML articles powered by AMS MathViewer

by Petr Štěpánek PDF
Trans. Amer. Math. Soc. 270 (1982), 131-147 Request permission

Abstract:

A simple construction of Boolean algebras with no rigid or homogeneous factors is described. It is shown that for every uncountable cardinal $\kappa$ there are ${2^\kappa }$ isomorphism types of Boolean algebras of power $\kappa$ with no rigid or homogeneous factors. A similar result is obtained for complete Boolean algebras for certain regular cardinals. It is shown that every Boolean algebra can be completely embedded in a complete Boolean algebra with no rigid or homogeneous factors in such a way that the automorphism group of the smaller algebra is a subgroup of the automorphism group of the larger algebra. It turns out that the cardinalities of antichains in both algebras are the same. It is also shown that every $\kappa$-distributive complete Boolean algebra can be completely embedded in a $\kappa$-distributive complete Boolean algebra with no rigid or homogeneous factors.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 06E05, 03E40
  • Retrieve articles in all journals with MSC: 06E05, 03E40
Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 270 (1982), 131-147
  • MSC: Primary 06E05; Secondary 03E40
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0642333-3
  • MathSciNet review: 642333