Unformatted text preview: { r ∈ R  r is nilpotent } . (a) Prove that Nil( R ) is a subring of R . (b) Prove that Nil( R ) is an ideal of R . (c) Prove that every prime ideal of R contains Nil( R ). (d) Prove that the quotient ring R/ Nil( R ) has no nonzero nilpotent elements. 3. An abelian group of order 8192 has elements of the following orders: order 1 2 4 8 16 32 # of elements 1 31 224 1792 2048 4096 Determine the isomorphism type of the group....
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 Spring '09
 Math, Algebra, Ring, Prime number, Ring theory, isomorphism type, ring R/ Nil

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