Let R be the ring Z[√−5]. (a) Prove that I = (2, 1 + √−5), the ideal generated by those two elements, is not a principal ideal. (b) Prove that I^2, the ideal generated by the squares of the elements in I is a principal ideal
Let R be the ring Z[√−5]. (a) Prove that I = (2, 1 + √−5), the ideal generated by those two elements, is not a principal ideal. (b) Prove that I^2, the ideal generated by the squares of the elements in I is a principal ideal
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.3: The Characteristic Of A Ring
Problem 22E: 22. Let be a ring with finite number of elements. Show that the characteristic of divides .
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Let R be the ring Z[√−5].
(a) Prove that I = (2, 1 + √−5), the ideal generated by those two elements,
is not a principal ideal.
(b) Prove that I^2, the ideal generated by the squares of the elements in I is
a principal ideal
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