Let D = {0,1,c,d} be an integral domain. Explain why the following are true: (1) If 4.1=0 then 2.1 = 0 characteristic of D is 2 x+x=0 for all x in D (iv) cd = 0 (v) cd # d and cd ‡ c (vi) cd = 1 Find the addition and multiplication tables for D han po zero divisors to
Let D = {0,1,c,d} be an integral domain. Explain why the following are true: (1) If 4.1=0 then 2.1 = 0 characteristic of D is 2 x+x=0 for all x in D (iv) cd = 0 (v) cd # d and cd ‡ c (vi) cd = 1 Find the addition and multiplication tables for D han po zero divisors to
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 1
Transcribed Image Text:Corollary 1.4.3
If F is a field, then F is either of characteristic a prime number p or of characteristic 0.
EXERCISE
1.
Let D = {0,1,c,d} be an integral domain. Explain why the following are true:
(1)
If 4.1=0 then 2.1 = 0
characteristic of D is 2
x+x=0 for all x in D
(iv)
cd = 0
(v)
cd # d and cd ‡ c
(vi)
cd = 1
Find the addition and multiplication tables for D
2.
Let 6.1 = 0 in an integral domain. Use the fact that D has no zero divisors to show
that either 2.1=0 or 3.1 = 0 implies that D has characteristic 2 or 3
Let D have characteristic 2. Show that
3.
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