Unformatted text preview: ab = 1, then ba must be also = 1. 3. Let A be a ring that is not an integral domain. Show that the ideal I = { f±A [ x ]  f (1) = 0 } is never a prime ideal. 4. Let R be a ring with 1 and with  R  ﬁnite. Show that then every element in R is either a unit or is a zerodivisor. 5. Find all solutions of x 28 x + 5 = 0 in Z / 10 Z . 1...
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 Summer '08
 JOSHUA
 Math, Algebra, Ring theory, Algebra Qualifying Exam, commutative integral domain

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