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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
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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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