16.1.12. Let I be the ideal generated by 3 in Z/36Z. Show that as a group I is isomorphic to (Z/12Z, +). Show that the ring I is not isomorphic to the ring (Z/12Z, +,). Similarly show that in Z/36Z, (6) is not isomorphic as a ring to Z/6Z.
16.1.12. Let I be the ideal generated by 3 in Z/36Z. Show that as a group I is isomorphic to (Z/12Z, +). Show that the ring I is not isomorphic to the ring (Z/12Z, +,). Similarly show that in Z/36Z, (6) is not isomorphic as a ring to Z/6Z.
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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