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Unformatted text preview: of R : C ( b ) = { a R : ab = ba } . 8. Give an example of a ring which is an integral domain but which is not a eld. 9. Prove that if f : R S is a homomorphism, then the following set is a subring of R : K = { a R : f ( a ) = 0 S } . 10. (Bonus) Let p be a prime. Prove that ( p1)! 1(mod p ). (This result is known as Wilsons theorem.) Hint: Prove that [ a ] = [ a ]1 if and only if [ a ] = [1] or [ a ] = [1]. (Compare with problem number 6 above.) Then use the fact that every nonzero element of Z p is a unit. 1...
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This note was uploaded on 09/08/2011 for the course MTH 310 taught by Professor R.bell during the Spring '10 term at Michigan State University.
 Spring '10
 R.Bell
 Algebra, Matrices

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