Let (R, +,.) be any ring. Define Rx Z = {(r,n):r ER,n E Z} and (r,n) + (s, m) = (r + s,m + n) (r,n). (s, m) = = (rs + rm + sn, nm) To show that (R × Z,+,.) is a ring: 1- V(r,n), (s, m) ER X Z → (r,n) + (s, m) = (r + s,m + n) ER x Z. 2-8 (H.W).
Let (R, +,.) be any ring. Define Rx Z = {(r,n):r ER,n E Z} and (r,n) + (s, m) = (r + s,m + n) (r,n). (s, m) = = (rs + rm + sn, nm) To show that (R × Z,+,.) is a ring: 1- V(r,n), (s, m) ER X Z → (r,n) + (s, m) = (r + s,m + n) ER x Z. 2-8 (H.W).
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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Transcribed Image Text:Let (R, +, .) be any ring. Define R × Z = {(r,n):r ER,n E Z} and
(r, n) + (s, m) = (r + s,m + n)
(r, n). (s, m)
= (rs + rm + sn, nm)
To show that (R × Z,+,.) is a ring:
1- V(r,n), (s, m) ER X Z
(r,n) + (s, m) = (r + s, m + n) ERXZ.
2-8 (H.W).
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