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.4251125(b) Is (2, 3), the ideal generated by 2 and 1/5, a principal ideal? Whatabout (2, 3)?

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Answered: 19.1.3. Recall that if a is any complex…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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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)?