1. Consider the ring Z₁2 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, with addition and multiplication modulo 12. (a) Find all of the cosets of the ideal I = an explanation of why you have found all of the cosets. (4) in Z12. Your answer should include (b) Compute the addition and multiplication tables of the factor ring Z₁2/(4) (choosing one name for each coset).
1. Consider the ring Z₁2 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, with addition and multiplication modulo 12. (a) Find all of the cosets of the ideal I = an explanation of why you have found all of the cosets. (4) in Z12. Your answer should include (b) Compute the addition and multiplication tables of the factor ring Z₁2/(4) (choosing one name for each coset).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:1. Consider the ring Z₁2 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, with addition and
multiplication modulo 12.
(a) Find all of the cosets of the ideal I
=
an explanation of why you have found all of the cosets.
(4) in Z12. Your answer should include
(b) Compute the addition and multiplication tables of the factor ring Z₁2/(4)
(choosing one name for each coset).
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