a) b) Z [V2] is an integral domain Show that S={(a,a) | a e Z} is a subring of Zx Z (Use the definition of addition and multiplication in direct products) Determine whether T = { { (a,- a) | ae Z) is a subring of ZxZ 7
a) b) Z [V2] is an integral domain Show that S={(a,a) | a e Z} is a subring of Zx Z (Use the definition of addition and multiplication in direct products) Determine whether T = { { (a,- a) | ae Z) is a subring of ZxZ 7
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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Number 3...
![3.
4
e)
Z [√2] is an integral domain
a)
Show that S = {(a,a) | a € Z } is a subring of Z x Z (Use the definition of
addition and multiplication in direct products)
b)
Determine whether T = {{ (a,- a) | ae Z) is a subring of Zx Z
7
Let R be a ring and consider R x Z-{(r,n) | reR, nez)
Define
(r,n) + (s,m) = (r+s, n + m)
(r, n)(s, m)
= (rs + mr + ns, nm)
Show that Rx Z is a ring](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9949b50e-c59e-4a5e-95ac-404b1c8ac983%2Fe6543ae0-3689-441b-b675-e01bc20e1e7b%2F62pc4um_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.
4
e)
Z [√2] is an integral domain
a)
Show that S = {(a,a) | a € Z } is a subring of Z x Z (Use the definition of
addition and multiplication in direct products)
b)
Determine whether T = {{ (a,- a) | ae Z) is a subring of Zx Z
7
Let R be a ring and consider R x Z-{(r,n) | reR, nez)
Define
(r,n) + (s,m) = (r+s, n + m)
(r, n)(s, m)
= (rs + mr + ns, nm)
Show that Rx Z is a ring
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