19.3.5. Let p(x) = x³ − x + 1 Є F2[x]. Let I = (p(x)), and let R = F2[x]/I. Let a=I+xЄ R. (a) Is p(x) irreducible in F2[x]? (b) How many elements does R have? (c) Is a a unit in R? (d) What is the additive order of a? What is the multiplicative order of a? (e) What is the characteristic of R?
19.3.5. Let p(x) = x³ − x + 1 Є F2[x]. Let I = (p(x)), and let R = F2[x]/I. Let a=I+xЄ R. (a) Is p(x) irreducible in F2[x]? (b) How many elements does R have? (c) Is a a unit in R? (d) What is the additive order of a? What is the multiplicative order of a? (e) What is the characteristic of R?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 32E
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