### Errata for 'Algebra: Chapter 0', second (2016) printing

This is the errata for the second (2016) printing of Chapter 0. If you are looking for the errata for the first (2009) printing, click here.

Highlighted in red are the needed changes, embedded in text matching the published version and identified by page and position on the page (e.g., `p.10, top'). A bold reference indicates an error in the published version which may be more confusing, such as a missing hypothesis in an exercise.

This list is bound to grow forever. (151 items so far.) The contribution of many readers of both printings is gratefully acknowledged.

Last updated: 6/27/24.

• #### Chapter I

• p.8, Exercise 1.3:

• p.15, Example 2.4:

• p.22, Example 3.4:

• p.27, Exercise 3.10:

• #### Chapter II

• p.44, bottom:

• p.56, Exercise 2.1:

• p.57, Exercise 2.10:

• p.57, Exercise 2.15, second point:

• p.61, middle:

• p.66, middle:

• p.77, bottom:

• p.81, top:

• p.83, footnote:

• p.87, Exercise 6.11:

• p.93, paragraph following Proposition 7.10:

• p.93, proof of Theorem 7.12:

• p.93, footnote:

• p.97, top:

• p.97, Proof of Corollary 8.2:

• p.102, footnote 37:

• p.105, Exercise 8.1:

• p.107, Exercise 8.17:

• p.108, bottom:

• p.109, beginning of section 9.2:

• p.110, bottom:

• p.112, bottom:

• p.113, Exercise 9.2:

• p.113, Exercise 9.3:

• p.113, Exercise 9.3:

• p.115, Exercise 9.17:

• #### Chapter III

• p.123, Proposition 1.12:

• p.129, bottom:

• p.132, middle:

• p.144, Exercise 3.9:

• p.146, bottom:

• p.147, Proof of Lemma 4.5:

• p.155, Exercise 4.17:

• p.156, beginning of section 5.

• p.163, Exercise 5.6:

• p.163, Exercise 5.11:

• p.172, Exercise 6.2:

• p.172, Exercise 6.6:

• p.172, Exercise 6.8:

• p.177, middle:

• #### Chapter IV

• p.192, second paragraph:

• p.197, second to last paragraph:

• p.200, middle:

• p.203, Exercise 2.4:

• p.205, Exercise 2.22:

• p.205, Exercise 2.23:

• p.205, Exercise 2.25:

• p.209, before Proposition 3.5:

• p.212, Corollary 3.13:

• p.214, beginning of section 4.1:

• p.226, Exercise 4.22:

• p.226, footnote:

• p.229, Definition 5.6:

• p.232, middle:

• p.237, Theorem 6.6, point 1:

• p.241, Exercise 6.8:

• #### Chapter V

• p.244, first paragraph of 1.1:

• p.244, bottom:

• p.246, middle:

• p.247, top:

• p.250, Exercise 1.7:

• p.250, Exercise 1.9:

• p.256, bottom:

• p.260, Exercise 2.20:

• p.265, first paragraph:

• p.267, Exercise 3.15:

• p.269, bottom:

• p.272, diagram:

• p.276, Exercise 4.6:

• p.277, second-to-last point of Exercise 4.7.

• p.280, Exercise 4.25:

• p.288, Proof of Proposition 5.17:

• p.290, Exercise 5.22:

• p.295, bottom:

• p.302, Exercise 6.19:

• #### Chapter VI

• p.309-10, proof of Proposition 1.9:

• p.310, bottom:

• p.314, Exercise 1.19:

• p.326, Exercise 2.10:

• p.328, middle:

• p.329, footnote 17:

• p.333, proof of Proposition 3.7:

• p.341, middle:

• p.343, bottom:

• p.347, Exercise 4.6:

• p.366, Lemma 6.14:

• p.367, bottom:

• p.370, top:

• p.371, Exercise 6.21:

• #### Chapter VII

• p.385, bottom:

• p.386, second paragraph:

• p.387, top:

• p.389, second paragraph:

• p.393, bottom:

• p.398, Exercise 1.15:

• p.410, top:

• p.414, Exercise 2.6:

• p.417, bottom:

• p.426, middle:

• p.431, Proof of Theorem 4.8:

• p.439, Exercise 4.8:

• p.459, top:

• p.465, bottom:

• p.471, bottom:

• p.473, end of first paragraph:

• p.474, top:

• p.476, top:

• p.476, Proof of Lemma 7.13:

• p.476-7, Proof of Proposition 7.14:

• p.480, Exercise 7.2:

• #### Chapter VIII

• p.491, second-to-last paragraph:

• p.495, bottom:

• p.497, Exercise 1.10:

• p.500, Exercise 1.28:

• p.509, bottom half:

• p.522, Exercise 3.15:

• p.526, middle:

• p.527, top half:

• p.532, Exercise 4.3:

• p.542, top:

• p.542, middle:

• p.544, Exercise 5.9:

• p.545, last line:

• p.547, middle:

• p.555, first display:

• #### Chapter IX

• p.578, top:

• p.593, top:

• p.596, proof of Lemma 3.4:

• p.596, first line following the proof of Lemma 3.4:

• p.599, middle:

• p.604, footnote:

• p.612, end of proof of Proposition 4.10:

• p.614, Exercise 4.5:

• p.639, Exercise 6.4:

• p.641, Exercise 6.13:

• p.643, middle:

• p.644, Proposition 7.3, statement:

• p.644, Proposition 7.3, proof:

• p.645, Remark 7.4:

• p.645, middle:

• p.655, middle:

• p.660, Exercise 7.14:

• p.663, statement of Theorem 8.3:

• p.668, Example 8.8:

• p.674, Theorem 8.12, first bullet:

• p.687, middle: