Let F be a field and let K be a subset of F with at least two elements. Prove that K is a subfield of F if, for any a,b (b not equal to 0) in K, a-b and ab-1 belong to K.
Let F be a field and let K be a subset of F with at least two elements. Prove that K is a subfield of F if, for any a,b (b not equal to 0) in K, a-b and ab-1 belong to K.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 8E: Let be an irreducible polynomial over a field . Prove that is irreducible over for all nonzero ...
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Let F be a field and let K be a subset of F with at least two elements. Prove that K is a subfield of F if, for any a,b (b not equal to 0) in K, a-b and ab-1 belong to K.
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