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Media type:
E-Article
Title:
Boolean Algebras with no Rigid or Homogeneous Factors
Contributor:
Štěpánek, Petr
imprint:
American Mathematical Society, 1982
Published in:Transactions of the American Mathematical Society
Language:
English
ISSN:
0002-9947
Origination:
Footnote:
Description:
<p>A simple construction of Boolean algebras with no rigid or homogeneous factors is described. It is shown that for every uncountable cardinal κ there are 2<sup>κ</sup>isomorphism types of Boolean algebras of power κ 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 κ-distributive complete Boolean algebra can be completely embedded in a κ-distributive complete Boolean algebra with no rigid or homogeneous factors.</p>