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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
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...
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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}, ×).
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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