NOTE: The corrections are written using LaTeX commands. The latest corrections were added in May, 1997. 3, line 12 For integers that can be represented read primes that can be represented 20, line 4 For Example 1.2.1 read Example 1.2.2 20, line -19 For every component read every exponent 24, line 10 For the proof of the theorem read the proof of the proposition 36, line 13 For compute $\varphi (24)$ read compute $\varphi (27)$ 42, line 9 For $| a_n - a_m | < 0$ read $| a_n - a_m | < \epsilon$ 53, line -14 For subset of $S \times T$ read subset of $S \times U$ 56, line 9 For $B = \{ f(x_1 ), f(x_1 ), \ldots, f(x_n ) \}$ read $B = \{ f(x_1 ), f(x_2 ), \ldots, f(x_n ) \}$ 65, line -10 For correspond to the equivalence classes $S/f$ read are the equivalence classes in $S/f$ 67, line 8 For Example 2.2.6 read Proposition 2.2.5 72, line 8 For It $\sigma \tau = \tau \sigma$ read If $\sigma \tau = \tau \sigma$ 80, line 8 For $ \frac{bd - ad}{c^2 + d^2} i $ read $ \frac{bc - ad}{c^2 + d^2} i $ 82, line 8 Correction: $ \sin \frac{\theta}{2} = \pm \sqrt{\frac{1 - \cos \theta}{2} } \cos \frac{\theta}{2} = \pm \sqrt{\frac{1 + \cos \theta}{2} } $ 82, line -2 Correction: $\cos (x) = 1-\frac{x^2}{2}+\frac{x^4}{4!}-\frac{x^6}{6!}+\ldots$ $\sin (x) = x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\dots$ 83, line -16 For never zero, it follows that $f$ is an entire function and hence read nonzero, it follows that $f$ is a bounded entire function and 84, line 1 For $z^3 +a_2 z +a_1 z +a_0$ read $z^3 +a_2 z^2 +a_1 z +a_0$ 101, line -12 For denoted by $SL_n (F)$ read denoted by $SL_n (R)$ 111, lines 12--13 For $Z_n$ of integers modulo $n$ read $Z_6$ of integers modulo $6$ 116, line -1 For $H = \{ [1],[3] \}$ read $H = \{ [1],[8] \}$ 128, line 17 For $p_1 < p_2 < \ldots < p_n$ read $p_1 < p_2 < \ldots < p_m$ 128, line -5 For $p_1 < p_2 < \ldots < p_n$ read $p_1 < p_2 < \ldots < p_m$ 132, line 22 For Section 2.2 read Section 2.3 137, line 1 For Section 2.2 read Section 2.3 142, line 18 For $\{ x \in G \mid \phi (x) = e \}$ read $\{ x \in G_1 \mid \phi (x) = e \}$ 154, line -11 For normal subgroup of $G$ read subgroup of $G$ 156, line 2 For elements $a$ of order $4$ and $b$ or read elements $a$ of order $4$ and $b$ of 166, line 17 For $ \ldots + (a_2 b_0 +a_1 b_1 +a_2 b_0) x^2 + $ read $ \ldots + (a_2 b_0 +a_1 b_1 +a_0 b_2) x^2 + $ 166, line 18 For $c_k$ of $f(x) g(x)$ read $c_k$ of $x^k$ in $f(x) g(x)$ 173, line 2 For $q(x), r(x) \in F$ read $q(x), r(x) \in F[x]$ 173, line 22 For $a_m b_{n-1} x^{m-n} g(x)$ read $a_m b_n^{-1} x^{m-n} g(x)$ 174, 12 For Example 4.2.4 read Example 4.2.2 175, line 3 For give us read gives us 179, line 8 For $x^2 + 2$ read $x^2 - 2$ 180, line 21 For polynomial with rational coefficients read polynomial with rational coefficients, such that $a_n$ and $a_0$ are nonzero 180, Exercise 11 Add (where $p$ is any prime number). 181, line 11 For $ \frac{c(x+d)}{(x^2+ax+b)^m} $ read $ \frac{cx+d}{(x^2+ax+b)^m} $ 181, line -8 For $c(x) + d(x) \mod p(x)) $ read $c(x) + d(x) (\mod p(x)) $ 181, line -7 For $c(x)d(x) ( \mod (x)) $ read $c(x)d(x) ( \mod p(x)) $ 182, line -12 For If $c$ is a root of $f(x)$ read If $c$ is an integral root of $f(x)$ 182, line -5 For $f(n) = q(n)(c-n)$, read $f(n) = q(n)(n-c)$, 182, line -3 For rational roots of equations such as read: integer (and thus rational) roots of monic equations such as 186, line 6 For $x^2 - 7 x^2 + 4x - 28 = 0$ read $x^3 - 7 x^2 + 4x - 28 = 0$ 209, line -4 and the remainder of the proof: For $D^{\times}$ read $D^{\ast}$ 211, line -8 For Define $+$ on $S$ read Define $+$ on $R_1$ 225, line 5 For domain read integral domain 239, line 18 For polynomials in $K[x]$ read nonzero polynomials in $K[x]$ 239, line 19 For polynomial $f(x) \in K[x]$ read nonzero polynomial $f(x) \in K[x]$ 239, line -7 For An ideal is prime read A nonzero ideal is prime 247, line 19 For polynomial $f(x) = a_0 +a_1 x + \ldots a_n x^n$ read nonzero polynomial $f(x) = a_0 +a_1 x + \ldots + a_n x^n$ 251, line -11 For Proposition 4.2.1 read Proposition 4.3.1 255, line -11 For mapped by $\phi$ to $t(x)$ read mapped by $\phi '$ to $t(x)$ 257, line -4 For finite field read finite fields 273, line 5 For $p|Z(G)|$ read $p | |Z(G)|$ 288, line 1 For adding $K_i$ read adding $H$ 290, line 1 For Let $G$ be a finite group read Let $G$ be a group 298, line 13 For page 298 line 13 where $\omega = (-1 + \sqrt 2 i )/2 $ read where $\omega = (-1 + \sqrt 3 i )/2 $ 303, line -4 For simple group $F^{\times}$ read cyclic group $F^{\times}$ 309, line 12 For $\theta \in \Gal (F/E)$ read $\theta \in \Gal (F/K)$ 309, line -12 For $\omega \sqrt[3]{2}, \omega \sqrt[3]{2}\}$ is a basis read $\omega \sqrt[3]{2}, \omega \sqrt[3]{4}\}$ is a basis 314, line 2 For $i = 2,3,\ldots,n-1$ read $i = 1,2,\ldots,n-1$ 314, line 8 For If $|\Gal (F/K)| = p$ read If $[F:K] = |\Gal (F/K)| = p$ 314, lines 10--11 For since $G$ is simple read since $[F:K]$ is prime 315, line 9 For $2, \ldots, n$ read $2, \ldots, m$ 316, lines 2--3 For Any element $\phi$ of $\Gal (E(\zeta) / K(\zeta))$ leaves $\zeta$ fixed, so $\phi (E) = E$ read For any $\phi \in \Gal (E(\zeta) / K(\zeta))$, $\phi (E) = E$ since $E$ is normal over $K$ 316, line 6 For $N_1 \supset \ldots \supset \{ 1 \} $ read $N_1 \supset \ldots \supset \{ e \} $ 317, line -4 For prime degree read prime degree $p$
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