Let R be a ring and let FCR be a subring. Suppose that F is a...
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Let R be a ring and let FCR be a subring. Suppose that F is a field. (When this happens, we say that R is an F-algebra.) Define scalar multiplication FXR → R by crer (where the right-hand side denotes ring multiplication). Prove that this scalar multiplication and the usual ring addition turns R into a vector space over F. Let R be a ring and let FCR be a subring. Suppose that F is a field. (When this happens, we say that R is an F-algebra.) Define scalar multiplication FXR → R by crer (where the right-hand side denotes ring multiplication). Prove that this scalar multiplication and the usual ring addition turns R into a vector space over F.
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Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Posted Date:
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