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

Answered: 16.1.12. Let I be the ideal generated…

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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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.