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Inverse limits of algebras as retracts of their direct products

Author: A. Laradji
Journal: Proc. Amer. Math. Soc. 131 (2003), 1007-1010
MSC (2000): Primary 08B25, 03E55
Published electronically: September 25, 2002
MathSciNet review: 1948088
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Abstract: Inverse limits of modules and, more generally, of universal algebras, are not always pure in corresponding direct products. In this note we show that when certain set-theoretic properties are imposed, they even become direct summands.

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

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  • 2. L. Fuchs, Infinite Abelian Groups I, Academic Press, New York, 1970. MR 41:333
  • 3. G. Grätzer, Universal Algebra, Second Edition, Springer-Verlag, New York, 1979. MR 80g:08001
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Additional Information

A. Laradji
Affiliation: Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received by editor(s): April 3, 2001
Received by editor(s) in revised form: October 26, 2001
Published electronically: September 25, 2002
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2002 American Mathematical Society

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