2 Consider The Ring R Z V5 A Bv5 A B E Z Define N R Z By N A B 5 A 562 It Has The Property N Ass 1 (71.92 KiB) Viewed 26 times
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(2) Consider the ring R = Z[V5] = {a +bV5 | a, b E Z}. Define N : R+ Z by N(a + b/5) = a– 562. It has the property N(aß) = N(a)N(B) for a, ß E R. (a) Show that R has infinitely many units. (b) Show that there is no a € R with N(a) = 2 (mod4). (c) Show that the ideal (2,1 + V5) is not principal. (d) Give an element of R that is irreducible, but not prime.
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