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14. (Activity 16.49). Let n Z, and define : Z→ Zn by ó(k)=[k]. (a) Show that Ker(6) = (n). We also denote this ideal as nZ. (b) Find Im(o). (c) Explain why ZZ/nZ. Page < 15 of 15 - ZOOM

14. (Activity 16.49). Let n Z, and define : Z→ Zn by ó(k)=[k]. (a) Show that Ker(6) = (n). We also denote this ideal as nZ. (b) Find Im(o). (c) Explain why ZZ/nZ. Page < 15 of 15 - ZOOM

Advanced Engineering Mathematics
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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14. (Activity 16.49). Let n € Z+, and define : Z → Zn by o(k) = [k]. (a) Show that Ker(p) = (n). We also denote this ideal as nZ. (b) Find Im(o). (c) Explain why Zn~Z/nZ. Page 15 of 15 ZOOM + »k
Transcribed Image Text:14. (Activity 16.49). Let n € Z+, and define : Z → Zn by o(k) = [k]. (a) Show that Ker(p) = (n). We also denote this ideal as nZ. (b) Find Im(o). (c) Explain why Zn~Z/nZ. Page 15 of 15 ZOOM + »k
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