19.3.4. Construct a field E with nine elements. Start with F3, find an irreducible polynomial of degree 2, and mod out by the ideal generated by the poly- nomial. Give the addition and multiplication tables of the field. Find two familiar groups that are isomorphic to (E,+) and (E – {0}, ×).
19.3.4. Construct a field E with nine elements. Start with F3, find an irreducible polynomial of degree 2, and mod out by the ideal generated by the poly- nomial. Give the addition and multiplication tables of the field. Find two familiar groups that are isomorphic to (E,+) and (E – {0}, ×).
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.6: Algebraic Extensions Of A Field
Problem 8E: If is a finite field with elements, and is a polynomial of positive degree over , find a formula...
Question
![19.3.4. Construct a field E with nine elements. Start with F3, find an irreducible
polynomial of degree 2, and mod out by the ideal generated by the poly-
nomial. Give the addition and multiplication tables of the field. Find two
familiar groups that are isomorphic to (E,+) and (E – {0}, ×).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5fbaae5-8d47-4476-8095-8b380294ae7e%2F3c6ad975-316d-4be8-82d6-8bad3e6763a2%2Fbukpv3f_processed.png&w=3840&q=75)
Transcribed Image Text:19.3.4. Construct a field E with nine elements. Start with F3, find an irreducible
polynomial of degree 2, and mod out by the ideal generated by the poly-
nomial. Give the addition and multiplication tables of the field. Find two
familiar groups that are isomorphic to (E,+) and (E – {0}, ×).
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