Mathematics 404A        Spring 2005

Typos in Artin

• p. 52, right after equation (4.7): It should say "The kernel of the homomorphism (4.2c)", not (4.2d).
• p. 57, "equation" (6.7): the last coset should be {x², y} -- note the comma.
• p. 71, problem 2.3.9: it should refer to Section 1, exercise 11, not Section 2, exercise 12.
• p. 73, problem 2.4.20(a): it should say SL₃, not SL_n.
• p. 84, last sentence of proof of (2.8): it should say "hence the left side b is divisible...", not "the left side a".
• p. 177, equation (5.3): it should say s' = gs, not that s' is an element of gs.
• p. 193, problem 5.5.11(a): it should say GL₂, not GL_n.
• p. 194, problem 5.6.7: the map from S to S' should be called "phi" (the map is unlabeled in the problem).
• p. 195, miscellaneous problem 3: "Int H" should be "Inn H".
• p. 361, item (iii) in the proof of (4.3). In the first equation, I-bar should be I.
• p. 398, second paragraph, lines 6 and 7: two inequalities should have a ≤ sign instead of a < sign: |x₀ + y₀|² &le 1/2, and the same inequality with a factor of |a|² included.
• p. 440, Theorem 12.10: the possibility that p=5 should be included ("either p=5 or p = ± 1 (modulo 5)")
• p. 443, problem 11.3.4: it should say "contains a nonzero integer".
• p. 444, problem 11.4.14: in part (a), n should be replaced by d.
• p. 445, problem 11.6.2: n^n-1 should be x^n-1.
• p. 492, after (1.2): the reference to [Chapter 11 (7.15)] should maybe be to [Chapter 11 (8.6)], together with the observation that the image of phi is a subring of K, and hence an integral domain.
• p. 494, a few lines after (2.2): the reference to [Chapter 11 (7.15)] should be to [Chapter 10 (7.3)]: since F[x]/(f(x)) is a field, the cited result says that (f(x)) must be maximal, from which it's easy to show that f(x) must be irreducible.
• p. 531, problem 13.2.4: F should be Q.
• p. 538, fourth paragraph: it should say "alpha + alpha' = -b".
• p. 541, proof of (1.14): the reference to (2.10) in Chapter 13 should be to (2.11) instead.
• p. 556, Lemma (5.1): in the phrase at the end of the statement "which sends alpha to a-tilde", a-tilde should be alpha-tilde.
• p. 576, problem 14.2.1: it should say "non-negative" intead of "positive".

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