Modern Algebra: An Introduction
Fifth Edition
John R. Durbin
John Wiley & Sons, 2005
Corrections to the first printing
The first list of corrections below involves errors in important facts that are the most likely
to cause confusion or affect the understanding of the text. The second list involves errors
that are less serious. Some changes to be made in the second printing, such as in spacing
or those involving the size of the font, are not listed below.
The total number of corrections is unfortunately large, due in part to problems in the
electronic transfer from the fourth to the fifth edition of the book. Regardless of the cause,
I apologize for the inconvenience.
JRD 8/04
durbin@math.utexas.edu
List 1.
p. 16. Example 2.1, line 4: α should be a.
p. 21. Following Example 3.5: “(b + c)” should be “a(b + c)” (to match the fourth edition).
p. 28. Problem 4.2, line 1: Second and third occurrences of a should be α.
p. 28. Problem 4.6, line 4: α should be a.
p. 112. Just above Table 22.2: “= N ρ1 ” should be “= N ρV ”.
p. 117. Second display: Insert “ Gk ” before second “=”.
p. 117. Line below second display: G should be Gi .
p. 120. Third line of first display in Definition: Second equation should be (a+b)c = ac+bc.
Also, it should be “for all a, b, c ∈ R”.
p. 121. Example 24.3: Replace third and fourth sentences by: “See Section 3. Problem
24.2 asks you to check one of the distributive laws. Multiplication for this ring is not
commutative.”
√
√
p. 128. Problem 25.21: b 3 4 should be c 3 4.
p. 148. Problem 31.13: 13.16 should be 13.19.
p. 184. Problem 39.9: In the second line, the second I should be J.
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p. 198. Proof of Theorem 43.2: Replace each ci by cij .
p. 200. Third line of second paragraph: “degree over” should be “degree n over”.
p. 208. Proof of Theorem 45.3: Second line of third paragraph, “= 1” should be “= −1”.
p. 209. Problem 45.1: Insert “of” after “group”.
p. 219. Proof of Theorem 47.2: In the fifth line, the first “p(x)” should be “p (x)”.
p. 222. Problem 47.11: C should be “the algebraic numbers”.
p. 227. Problem 49.9: Insert “(1)” as an element of N .
p. 239. Last line of last display: first term should be πh−1 g (s).
p. 275. Line 4 of Example 60.1: pq = 10, 403.
p. 275. Example 60.2: In step 6, the exponent should be 1183.
p. 276. Example 60.2: Again, in step 6, the exponent should be 1183.
p. 278. In seventh line after Figure 61.1, “modulo n” should be “modulo p”.
p. 325. In (D.2), (β(v)) should be β(α(v)).
List 2.
p. 25. Problem 3.29, display: ) should be }.
p. 50. Notes on Chapter II, line 4: 48 should be 49.
p. 93. Problem 17.33: Parenthetical remark should be “(See Theorem 15.4.)”.
p. 105. Delete the second “1.”.
p. 124. Problem 24.4: Insert ( before “Here”.
p. 132. Line 8: “group” should be “groups”.
p. 144. In the first line of the display, delete the comma following [a, b].
p. 150. In the third line of the display in the Proof, the second occurrence of adf should
be acf .
p. 165. Example 35.1:
3
2x
should be 32 x2 .
p. 182. Fifth line of the Proof: 1 should be I.
p. 186. Sixth line from the bottom: 1 + x should be I + x.
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p. 190. Second paragraph: [51] should be [5].
p. 197. Problem 42.11: insert “b = 0” at the end of the first sentence.
p. 200. Near the end of first paragraph: “one,” should be “one;”.
p. 207. Second line after Table 45.4: a should be α.
p. 209. Last line before Problems: Change to “1 + α, 1 + 2α, 2 + α, and 2 + 2α are all
generators.”
p. 212. First line of the Proof: (1) should be σ(1).
p. 213. Theorem 46.2: In the last line, ( should be {.
p. 214. Third line: “realtions” should be “relations”.
p. 215. Line following Figure 46.2: Delete “which closes this section,”.
p. 215. Immediately preceding Lemma 46.1: “in the preceding paragraph” should be
“preceding Example 46.3”.
p. 219. Theorem 47.2: “IF” should be “If F ”.
p. 220. Next to last line: “F (d t)” should be “F (d)”.
p. 221. Proof of Theorem 47.7: ≤ should be ⊆, both times.
p. 227. Third line: “by Theorem 44.6” should be “(Section 44)”.
p. 233. Second line before Theorem 51.1: (50.2) should be (51.2).
p. 238. Second line before Definition: Insert “for” before “composition”.
p. 240. Problem 53.4: Replace ( by {.
p. 241. Problems 53.14(b) and 53.15(b): Remove parentheses around “s ∼G t” and “s ∼H t”,
respectively.
p. 321. Example C.2: In the third from the last line, “P k” should be “P (k)”.
p. 322. Next to the last line: replace the period by a comma at the end.
p. 325. Third line after Theorem D.1: “respectively, if” should be “respectively. If”.
p. 346. “Ker” should be “Ker θ”.
p. 353. Second line of second column: “polynomials” should be “polynomial”.
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