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Inverse limits of algebras as retracts of their direct products
Author(s):
A.
Laradji
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1007-1010.
MSC (2000):
Primary 08B25, 03E55
Posted:
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:
-
- 1.
- L. Fuchs, Note on linearly compact abelian groups, J. Austral. Math. Soc. 9 (1969), 433-440. MR 39:6979
- 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
- 4.
- T. Jech, Set Theory, Academic Press, New York, 1978. MR 80a:03062
- 5.
- A. Levy, Basic Set Theory, Springer-Verlag, Berlin, 1979. MR 80k:04001
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Additional Information:
A.
Laradji
Affiliation:
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Email:
alaradji@kfupm.edu.sa
DOI:
10.1090/S0002-9939-02-06666-2
PII:
S 0002-9939(02)06666-2
Received by editor(s):
April 3, 2001
Received by editor(s) in revised form:
October 26, 2001
Posted:
September 25, 2002
Communicated by:
Carl G. Jockusch, Jr.
Copyright of article:
Copyright
2002,
American Mathematical Society
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