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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.

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
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.7: Direct Sums (optional)
Problem 1E: Let H1={ [ 0 ],[ 6 ] } and H2={ [ 0 ],[ 3 ],[ 6 ],[ 9 ] } be subgroups of the abelian group 12 under...
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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.
Transcribed Image Text: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.
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