Free module: Difference between revisions

Revision as of 21:13, 3 April 2004

Revision as of 22:49, 27 May 2004

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Note that an immediate [[corollary]] of (2) is that the coefficients in (1) are unique for each ''x''.

The definition of an infinite free basis is similar, except that ''E'' will have infinitely many elements. In generalBut, the summation which generates the elements ''x'' of ''M'' may be infinite but must converge in whatever sense is appropriate for ''M''. For some modules this will mean that it must be a finite sum, and thus that for any particular ''x'' only finitely many of the elements of ''E'' are involved.

In the case of an infinite basis, the rank of ''M'' is the [[cardinality]] of ''E''.

[[es:Módulo libre]]