prove that Z[x]/(x2+1)≃Z[i], where Z[i]={a+b√-1|a,b∈Z}. show only injectivity and surjectivity in terms of φ:Z[x]/(x^2+1)→Z[i]. (For example 2+3x+x3(x2+1)→2+3i)
prove that Z[x]/(x2+1)≃Z[i], where Z[i]={a+b√-1|a,b∈Z}. show only injectivity and surjectivity in terms of φ:Z[x]/(x^2+1)→Z[i]. (For example 2+3x+x3(x2+1)→2+3i)
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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prove that Z[x]/(x2+1)≃Z[i], where Z[i]={a+b√-1|a,b∈Z}.
show only injectivity and surjectivity in terms of φ:Z[x]/(x^2+1)→Z[i]. (For example 2+3x+x3(x2+1)→2+3i)
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