Proof that Let K be a ring with identity and Fa free K-module with an infinite denumerable
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Proof that Let K be a ring with identity and Fa free K-module with an infinite denumerable basis {e1,e2, ... }. Then R = HomK(F,F) is a ring by Exercise 1. 7(b). If n is any positive integer, then the free left R-module R has a basis of n elements; that is, as an R-module, R ≅ R⊕• • • ⊕ R for any finite number of summands.
Data from Exercise 1.7(b)
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To determine that the free left Rmodule R has a basis of n elements maximize the fact that the Hom f...View the full answer
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Related Book For 
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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