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 November 25th, 2006, 05:41 PM #1 Newbie   Joined: Nov 2006 From: USA Posts: 7 Thanks: 0 Unique factorization Domain Let R be the quadratic integer ring Z[sqrt(-5)] and define the ideals I_2=(2, 1 + sqrt(-5)); I_3=(3, 2 + sqrt(-5)); I'_3=(3, 2 - sqrt(-5)); a) Prove that I_2, I_3, I'_3 are prime ideals in R. b) Show that the factorizations 6=2.3=(1+sqrt(-5))(1-sqrt(-5)) imply the equality of ideals (6)=(2)(3) and (6)=(1+sqrt(-5))(1-sqrt(-5)). Show that these two ideal factorizations give the same factorization of the ideal (6) as the product of prime ideals. Tags domain, factorization, unique Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post rayman Abstract Algebra 2 October 19th, 2012 06:38 AM Lokokatz3nkl0 Number Theory 1 September 10th, 2012 05:12 AM squelchy451 Number Theory 1 July 3rd, 2010 03:42 AM good_phy Calculus 1 October 12th, 2008 09:26 AM Ann New Users 0 December 31st, 1969 04:00 PM

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