### Errata for 'Algebra: Chapter 0'

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. (My personal favorite is the missing abelian on p.49, Exercise 1.8.)

This list is bound to grow forever. (267 items, and counting.) The contribution of many readers is hereby gratefully acknowledged.

Last updated: 5/1/16.

• #### preface

• p.xvii, end of first paragraph:

• #### Chapter I

• p.8, Exercise 1.2:

• p.9, middle:

• p.9, bottom:

• p.10, top:

• p.11, middle:

• p.13, middle:

• p.16, bottom half:

• p.17, Exercise 2.2:

• p.21, middle:

• p.23, middle:

• p.33, middle:

• #### Chapter II

• p.44, top:

• p.49, Exercise 1.8:

• p.52, second-to-last paragraph:

• p.54, middle:

• p.55, Remark 2.4:

• p.56, Exercise 2.1:

• p.57, Exercise 2.6:

• p.57, Exercise 2.12:

• p.58, Exercise 2.18:

• p.60, middle:

• p.63, Exercise 3.1:

• p.63, Exercise 3.9:

• p.65, bottom:

• p.68, middle:

• p.69, top:

• p.69, Exercise 4.2:

• p.70, Exercise 4.14:

• p.70, Exercise 4.16:

• p.72, top:

• p.79, bottom:

• p.80, Lemma 6.3:

• p.80, middle:

• p.81, proof of Proposition 6.6:

• p.81, Remark 6.7:

• p.81, bottom half:

• p.82, top:

• p.83, middle:

• p.85, Exercise 6.1:

• p.86, Exercise 6.3:

• p.87, Exercise 6.14:

• p.88, Exercise 6.15:

• p.92, middle:

• p.94, bottom half:

• p.99, bottom half:

• p.104, bottom half:

• p.106, Exercise 8.9:

• p.107, Exercise 8.13:

• p.107, Exercise 8.15:

• p.111, Proposition 9.9:

• p.113, Exercise 9.1:

• p.116, top:

• #### Chapter III

• p.120, top:

• p.125, bottom:

• p.126, bottom:

• p.127, Exercise 1.3:

• p.127, Exercise 1.4:

• p.130, footnote:

• p.131, middle:

• p.132, middle:

• p.133, middle:

• p.136, bottom:

• p.137, Exercise 2.11:

• p.138, Exercise 2.17:

• p.139, middle:

• p.144, Exercise 3.15:

• p.149, Example 4.8:

• p.152, middle:

• p.153, top:

• p.154, top:

• p.154, Exercise 4.9:

• p.154, Exercise 4.10:

• p.160, bottom:

• p.162, Proposition 5.17:

• p.163, Exercise 5.5:

• p.163, Exercise 5.6:

• p.164, Exercise 5.17:

• p.167, bottom half:

• p.173, top:

• p.173, Exercise 6.10:

• p.173, Exercise 6.11:

• p.174, Exercise 6.17:

• p.179, bottom:

• p.181, middle:

• p.184, Exercise 7.11:

• p.184, Exercise 7.12:

• p.185, Exercise 7.13:

• #### Chapter IV

• p.195, bottom half:

• p.196, Definition 2.3:

• p.196, first paragraph of 2.2:

• p.196, second paragraph of 2.2:

• p.199, Theorem 2.11:

• p.201, middle:

• p.201, bottom half:

• p.203, Exercise 2.4:

• p.203, Exercise 2.13:

• p.205, Exercise 2.22:

• p.205, Exercise 2.23:

• p.205, bottom:

• p.206, top:

• p.207, top:

• p.209, top:

• p.209, middle:

• p.212, Corollary 3.13:

• p.212, bottom:

• p.220, Lemma 4.12:

• p.221, top half:

• p.224, middle:

• p.226, Exercise 4.19:

• p.227, top:

• p.229, Definition 5.6:

• p.232, proof of Proposition 5.11:

• p.233, Exercise 5.3:

• p.234, bottom half:

• p.234, Exercise 5.17:

• p.237, Theorem 6.6:

• p.239, Lemma 6.9:

• p.239, middle:

• p.239, Theorem 6.10:

• p.241, Exercise 6.10:

• #### Chapter V

• p.245, top half:

• p.247, top half:

• p.247, bottom half:

• p.247, bottom half:

• p.250, Exercise 1.12:

• p.250, Exercise 1.13:

• p.251, Exercise 1.17:

• p.255, middle:

• p.257, bottom:

• p.258, top half:

• p.259, Exercise 2.10:

• p.260, Exercise 2.19:

• p.260, Exercise 2.20:

• p.261, first paragraph of 3.1:

• p.264, bottom:

• p.265, Proof of Proposition 3.5:

• p.267, Exercise 3.13:

• p.269, bottom:

• p.272, middle:

• p.274, proof of Lemma 4.15:

• p.277, bottom:

• p.278, Exercise 4.10:

• p.278, Exercise 4.12:

• p.281, top:

• p.282, top:

• p.285, Lemma 5.10:

• p.286, top:

• p.288, Proof of Proposition 5.17:

• p.289, Exercise 5.1:

• p.289, Exercise 5.3:

• p.290, Exercise 5.8:

• p.290, Exercise 5.11:

• p.292, proof of Lemma 6.2:

• p.292, proof of Lemma 6.3:

• p.299, middle:

• p.300, Exercise 6.3:

• p.301, third bullet of Exercise 6.8:

• p.301, Exercise 6.9:

• p.301, Exercise 6.12:

• p.303, Exercise 6.21:

• #### Chapter VI

• p.308, top:

• p.311, middle:

• p.312, Exercise 1.3:

• p.312, Exercise 1.4:

• p.313, Exercise 1.15:

• p.316, top:

• p.317, footnote:

• p.319, bottom:

• p.334, proof of Claim 3.10:

• p.349, Exercises 4.15-4.16:

• p.350, Lemma 5.2:

• p.351, middle:

• p.354, Theorem 5.6:

• p.356, middle:

• p.358, Exercise 5.8:

• p.364, bottom:

• p.368, Exercise 6.4:

• p.370, Exercise 6.16:

• p.370, Exercise 6.18:

• p.370, footnote:

• p.371, Exercise 6.22:

• p.378, following the proof:

• p.383, Exercise 7.16:

• p.383, Exercise 7.16:

• #### Chapter VII

• p.387, bottom:

• p.388, top half:

• p.389, Proposition 1.5:

• p.391, Definition 1.8:

• p.393, Example 1.12:

• p.397, Exercise 1.6:

• p.397, Exercise 1.8:

• p.400, Exercise 1.29:

• p.402, proof of Claim 2.5:

• p.403, top:

• p.403, bottom:

• p.404, top:

• p.411, top:

• p.421, proof of Lemma 3.3:

• p.423, bottom:

• p.436, beginning of 4.3:

• p.439, bottom:

• p.446, near the top:

• p.447, end of proof of Corollary 5.12:

• p.448, proof of Proposition 5.16:

• p.449, Example 5.17:

• p.450, top:

• p.450, bottom:

• p.452, second line of Exercise 5.7:

• p.452, first line of Exercise 5.11:

• p.453, top:

• p.457, Proof of Theorem 6.9:

• p.464, middle:

• p.466, Exercise 6.2:

• p.472, top:

• p.476, bottom:

• p.478, third paragraph:

• p.481, Exercise 7.11:

• #### Chapter VIII

• p.489, top:

• p.490, bottom:

• p.492, bottom:

• p.496, Exercise 1.5:

• p.497, Exercise 1.7:

• p.497, Exercise 1.9:

• p.497, Exercise 1.11:

• p.498, Exercise 1.12:

• p.505, Corollary 2.6:

• p.521, Exercise 3.9:

• p.522, Exercise 3.15:

• p.525, bottom:

• p.526, top half:

• p.529, (iv)=>(ii):

• p.529, middle:

• p.533, Exercise 4.12:

• p.535, Exercise 4.22:

• p.538, Proof of Proposition 5.5:

• p.540, bottom:

• p.543, Exercise 5.3:

• p.544, Exercise 5.12:

• p.544, Exercise 5.13:

• p.546, Lemma 6.2:

• p.549, bottom:

• p.550, Proof of Lemma 6.9:

• p.554, beginning of Section 6.5:

• p.555, Exercise 6.5:

• p.557, Exercise 6.22, last bullet:

• #### Chapter IX

• p.563, bottom:

• p.563, Lemma 1.5:

• p.567, bottom:

• p.568, bottom:

• p.569, middle:

• p.574, Exercise 1.8:

• p.575, top:

• p.575, Exercise 1.14:

• p.580, top row of the diagram:

• p.580, bottom half:

• p.582, top:

• p.584, bottom:

• p.591, Exercise 2.17:

• p.602, Exercise 3.1:

• p.614, top:

• p.614, Exercise 4.5:

• p.629, middle:

• p.651, bottom:

• p.661, hint to Exercise 7.15:

• p.662, Example 8.2:

• p.663, bottom:

• p.695, Exercise 9.2: