- 5 A Compute The Group Of Units In The Ring 2 9z Prove That Z 9z Is Not An Integral Domain B Compute The Group Of 1 (21.23 KiB) Viewed 25 times
(5) (a) Compute the group of units in the ring 2/9Z. Prove that Z/9Z is not an integral domain. (b) Compute the group of
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(5) (a) Compute the group of units in the ring 2/9Z. Prove that Z/9Z is not an integral domain. (b) Compute the group of
(5) (a) Compute the group of units in the ring 2/9Z. Prove that Z/9Z is not an integral domain. (b) Compute the group of units in the ring Z/5Z. Prove that Z/5Z is an integral domain and a field. (6) Consider the following set of real numbers Z[V5] = {a +bV5:,bez} with the usual addition and multiplication of real mumbers. Define the function N:Z[V5Z by N(a+bV5) = 22 - 562 (a) Let 1 = 2 - 3/5 and y = 4-V5. Computer + y and xy and N(x). (b) Prove that Z[V3) is a subring of the ring of real numbers. (c) Prove that if r = a +b/5 and y =c+ 5, then N(x) = N(x)N(). :
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