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Unformatted text preview: R module endomor-phism of M is an R module homomorphism from M to M . Notation 8.1.22. The set of all R module homomorphisms from M to N is denoted by Hom R .M;N/ . The set of all R module endomoprhisms of M is denoted by End R .M/ . The kernel of an R module homomorphism ' W M ! N is f x 2 M W '.x/ D g . Example 8.1.23. Suppose R is a commutative ring. For any natural num-ber n , consider R n as the set of n by 1 matrices over R (column vec-tors). Let T be a xed n by m matrix over R . Then left multiplication by T is an R-module homomorphism from R m to R n . Example 8.1.24. Fix a ring R . Let T be a xed n by m matrix with entries in Z . Then left multiplication by T maps R m to R n , and is an R-module homomorphism even if R is non-commutative....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
- Fall '08