List of typos found in contemporary abstract algebra, 10th edition.
- p78 ch 4 example 4, instead of $\langle 1 \rangle = \langle 1 \rangle$, we should have $\langle 1 \rangle = \{ 1
\}$
- p131 Ch 6 Ex 6 In step 2, change {$MAM = MBA\inv$} to $MAM = MBM\inv$
- p132 Ch 6 Thm 6.1 Part 7, change {$G$ and $G$} to $G$ and $\overline{G}$
- p138 Ch 6 Thm 6.4 at the end with the $T(\alpha
\beta)$ stuff, at the underbrace, change it to $\beta(1)$ times.
Specifically $\underbrace{\alpha(1 + 1 + \cdots + 1)}_{\beta(1)}$ becomes
$\underbrace{\alpha(1 + 1 + \cdots + 1)}_{\beta(1) \text{ times}}$ (Fixing
the other one is left as an exercise)
- p165 ch 7 ex 32 On the last line, change
"or order 2" to "of order 2".
-
p187 ch 8 ex 39 On the first line, $G$ should
be $\set{3^m 6^n \mid m, n \in Z}$ instead of $\set{3^m 6^m \mid m, n \in
Z}$. Similar issue with the last line.
-
p187 ch8 ex 40 There is a missing bracket.
The corrected bit should look like $\abs{\paren{a_1, a_2, \dots, a_n}} =
\infty$
-
p221 ch 10 thm 10.1 On point 2, add in the
missing brace. It should look like $\phi\paren{g^n} = \paren{\phi(g)}^n$
instead.
-
p221 ch 10 thm 10.1 At the beginning of the
proof of property 3, insert "Let $\overline e$ be the identity of $\overline
G$.
-
p221 ch 10 thm 10.1 At the line "imply that $e
= \phi\paren e = \phi\paren{g^n} = \paren{\phi(g)}^n$", add an overline over
the $e$ at the start to look like:
\[ \overline e = \phi\paren e = \phi\paren{g^n} = \paren{\phi(g)}^n \]
-
p223 ch 10 ex 8 \[
\operatorname{sgn}\paren\sigma = \begin{cases}
+1 &\text{if $\sigma$ is an even permutation} \\
-1 &\text{if $\sigma$ is an even permutation}
\end{cases}
\]
Change the second even to odd.
-
p247 ch11 lemma 2 At the line "Since $b$ was
chosen to have smallest order such that $b \in \gen a$", change it to $b
\notin \gen a$.
-
p247 ch 11 lemma 2 At the line "For if $x \in \gen
a \cap K$, then $\overline x \in \gen{\overline a} \cap \overline K =
\set{\overline e} = ${$\gen b$}", change $\gen b$ to $\{\gen b\}$
-
p249 ch 11 lemma 4 At the line "Since ($n' = M'$)"
change the $M'$ to $m'$
-
p262 ch 12 ex 20 Change $R_0 \subset R_1
\subset R_2 \cdots$ to $R_0 \supset R_1 \supset R_2 \cdots$
-
p274 ch 13 exercises Exercises 15 and 16 are
duplicated (Chapter 12 Exercises 30 and 31) respectively
-
p289 ch 14 ex 41 Change "communitive" to
"commutative"
-
p307 ex 50 If $R$ is a field prove the mapping is an isomorphism. Without the assumption that $R$ is finite,
it is impossible.
See Wikipedia and Math
StackExchange
-
p307 ex 53a Change $\phi -1 (A)$ to $\phi\inv(A)$
-
p 320 ch 16 ex 14 Change "the converse is to not
true" to "the converse is not true"
-
p 321 ch 16 ex 29 Change "give an example of be a
commutative ring" to "give an example of a commutative ring".
-
p 344 ch 18 example 1 "so that $1 + \sqrt{-3}$ divides $2 \cdot 2$" add in the missing word "means": "so that
means $1 + \sqrt{-3}$ divides $2 \cdot 2$"
-
p 353 ch 18 example 4 Change $p_2$ to $p^2$. See Theorem 16.4 for Eisenstein's Criterion.
-
p 367 ch 19 line 19 Change $-1 + \langle x^2 = 1 \rangle$ to $-1 + \langle x^2 + 1 \rangle$.
possible improvements
-
p 326 example 3 "Since 1 is the only divisor of 40 that is congruent to 1 modulo 5"... Note that we only
should be considering divisors of 40/5 by Sylow's 3rd Theorem.