19.1.3. Recall that if a is any complex number, then Z[a] = {p(a) | p(x) = Z[x]}. Let R = Z[]. (a) Show that 12+ 3+ + Є R. 4 25 1 125 (b) Is (2, 3), the ideal generated by 2 and 1/5, a principal ideal? What about (2, 3)?
19.1.3. Recall that if a is any complex number, then Z[a] = {p(a) | p(x) = Z[x]}. Let R = Z[]. (a) Show that 12+ 3+ + Є R. 4 25 1 125 (b) Is (2, 3), the ideal generated by 2 and 1/5, a principal ideal? What about (2, 3)?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 56E
Question
![19.1.3. Recall that if a is any complex number, then Z[a] = {p(a) | p(x) = Z[x]}.
Let R = Z[].
(a) Show that 12+ 3+ + Є R.
4
25
1
125
(b) Is (2, 3), the ideal generated by 2 and 1/5, a principal ideal? What
about (2, 3)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5fbaae5-8d47-4476-8095-8b380294ae7e%2F86eb0e4c-f33f-4764-86d3-f2b2494f7c6f%2Fm2om32j_processed.png&w=3840&q=75)
Transcribed Image Text:19.1.3. Recall that if a is any complex number, then Z[a] = {p(a) | p(x) = Z[x]}.
Let R = Z[].
(a) Show that 12+ 3+ + Є R.
4
25
1
125
(b) Is (2, 3), the ideal generated by 2 and 1/5, a principal ideal? What
about (2, 3)?
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