31. Let F be a field and f(x), g(x) e F[x]. Show that f(x) divides g(x) if and only if g(x)E (f(x)). 32. Let F he a field ond
31. Let F be a field and f(x), g(x) e F[x]. Show that f(x) divides g(x) if and only if g(x)E (f(x)). 32. Let F he a field ond
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Section 27: Number 31
![every proper nontrivial prime ideal of F[x] is maximal.
31. Let F be a field and f(x), g(x) e F[x]. Show that f(x) divides g(x) if and only if g(x) E (ƒ(x)).
32. Let F be a field and let f(x), g(x) e F[x]. Show that
N = {r(x)f(x)+ s(x)g(x)|r(x), s(x) E F[x]}
is an ideal of F[x]. Show that if f(r)and alu) I](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4dd8e23-ab66-4b24-8e54-a64daec9031c%2F8587662a-f2b9-4715-abdc-cacf4ba2049c%2Fsx4h1l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:every proper nontrivial prime ideal of F[x] is maximal.
31. Let F be a field and f(x), g(x) e F[x]. Show that f(x) divides g(x) if and only if g(x) E (ƒ(x)).
32. Let F be a field and let f(x), g(x) e F[x]. Show that
N = {r(x)f(x)+ s(x)g(x)|r(x), s(x) E F[x]}
is an ideal of F[x]. Show that if f(r)and alu) I
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