Theory 9.) Let K be an algebraically closed field. Show that every isomorphism ơ of K onto a subfield of itself such that K is algebraic over o [K]is an automorphism of K, that is, is an onto map. [Hint: Apply Theorem 49.3 to o 10. Let E be an algebraic extension of a field F. Show that every isomorphism of E onto a subfield of F leaving F fixed car be extended to an automorphism of F. E ond E of F and E,
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.
Number 9:
![Theory
9.) Let K be an algebraically closed field. Show that every isomorphism o of K onto a subfield of itself such that
K is algebraic over o [K]is an automorphism of K, that is, is an onto map. [Hint: Apply Theorem 49.3 too".]
10. Let E be an algebraic extension of a field F. Show that every isomorphism of E onto a subfield of F leaving
S fixed can be extended to an automorphism of F.
olgebraic closures F and E of F and E,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4dd8e23-ab66-4b24-8e54-a64daec9031c%2F26269440-b150-4263-8768-f64ab2ed8cf2%2Fn62o1wk_processed.jpeg&w=3840&q=75)
Let K be an algebraically closed field. We have to show that every isomorphism of K onto a subfield of itself such that K is algebraic over is an automorphism of K that is, is an onto map.
To prove this we will use Isomorphism Extension Theorem,that says:
"Consider E be an algebraic extension of field F. Let be an isomorphism of F onto the field F'. Let be an algebraic closure of F'. Then can be extended to an isomorphism of E onto a subfield of such that for all ."
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