MAS4002 Algebraic Number Theory: Errata to Problem sheets

Sheet 1, question 9 (viii) should read: X^{4} + 3X^{3} + 2X^{2} + 3. Sheet 1, the second question 11 should be (of course) question 12. Sheet 2, question 15. α should be 1 + \sqrt{−5} not \frac{1}{2}(1 + \sqrt{−5}) which, as you

should realize, is not an algebraic integer. As a consequence J_{2} should be defined as ⟨3, 2 − α⟩. Better still forget about α and define I = ⟨2, 1 + \sqrt{−5}⟩ J_{1} = ⟨3, 1 + \sqrt{−5}⟩ and J_{2} = ⟨2, 1 − \sqrt{−5}⟩.

RJC 22/3/2000