### Errata for 'Algebra: Chapter 0', first (2009) printing

This is the errata for the first (2009) printing of Chapter 0. If you are looking for the errata for the second (2016) 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. (My personal favorite is the missing abelian on p.49, Exercise 1.8.)

This list is bound to grow forever. (403 items, and counting.) The contribution of many readers is hereby gratefully acknowledged.

Last updated: 6/27/24.

• #### preface

• p.xvii, end of first paragraph:

• #### Chapter I

• p.8, Exercise 1.2:

• p.8, Exercise 1.3:

• p.9, middle:

• p.9, bottom:

• p.10, top:

• p.11, middle:

• p.13, middle:

• p.15, Example 2.4:

• p.16, bottom half:

• p.17, Exercise 2.2:

• p.21, middle:

• p.22, Example 3.4:

• p.23, middle:

• p.27, Exercise 3.10:

• p.33, middle:

• #### Chapter II

• p.44, top:

• p.44, bottom:

• 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 2.10:

• p.57, Exercise 2.12:

• p.57, Exercise 2.15, second point:

• p.58, Exercise 2.18:

• p.60, middle:

• p.61, middle:

• p.63, Exercise 3.1:

• p.63, Exercise 3.9:

• p.65, bottom:

• p.66, middle

• 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.77, bottom:

• p.79, bottom:

• p.80, Lemma 6.3:

• p.80, middle:

• p.81, top:

• p.81, proof of Proposition 6.6:

• p.81, Remark 6.7:

• p.81, bottom half:

• p.82, top:

• p.83, middle:

• p.83, footnote:

• p.85, Exercise 6.1:

• p.86, Exercise 6.3:

• p.87, Exercise 6.11:

• p.87, Exercise 6.14:

• p.88, Exercise 6.15:

• p.92, middle:

• p.93, paragraph following Proposition 7.10:

• p.93, proof of Theorem 7.12:

• p.93, footnote:

• p.94, bottom half:

• p.97, top:

• p.97, Proof of Corollary 8.2:

• p.99, bottom half:

• p.102, footnote 37:

• p.104, bottom half:

• p.105, Exercise 8.1:

• p.106, Exercise 8.9:

• p.107, Exercise 8.13:

• p.107, Exercise 8.15:

• p.107, Exercise 8.17:

• p.108, bottom:

• p.109, beginning of section 9.2:

• p.110, bottom:

• p.111, Proposition 9.9:

• p.112, bottom:

• p.113, Exercise 9.1:

• p.113, Exercise 9.2:

• p.113, Exercise 9.3:

• p.113, Exercise 9.3:

• p.115, Exercise 9.17:

• p.116, top:

• #### Chapter III

• p.120, top:

• p.123, Proposition 1.12:

• p.125, bottom:

• p.126, bottom:

• p.127, Exercise 1.3:

• p.127, Exercise 1.4:

• p.129, bottom:

• 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 3.9:

• p.144, Exercise 3.15:

• p.146, bottom:

• p.147, Proof of Lemma 4.5:

• 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.155, Exercise 4.17:

• p.156, beginning of section 5.

• p.160, bottom:

• p.162, Proposition 5.17:

• p.163, Exercise 5.5:

• p.163, Exercise 5.6:

• p.163, Exercise 5.11:

• p.164, Exercise 5.17:

• p.167, bottom half:

• p.172, Exercise 6.2:

• p.172, Exercise 6.6:

• p.172, Exercise 6.8:

• p.173, top:

• p.173, Exercise 6.10:

• p.173, Exercise 6.11:

• p.174, Exercise 6.17:

• p.177, middle:

• p.179, bottom:

• p.181, middle:

• p.184, Exercise 7.11:

• p.184, Exercise 7.12:

• p.185, Exercise 7.13:

• #### Chapter IV

• p.192, second paragraph:

• p.195, bottom half:

• p.196, Definition 2.3:

• p.196, beginning of 2.2:

• p.197, second to last paragraph:

• p.199, Theorem 2.11:

• p.200, middle:

• p.201, middle:

• p.201, bottom half:

• p.203, Exercise 2.4:

• p.203, Exercise 2.9:

• p.203, Exercise 2.13:

• p.205, Exercise 2.22:

• p.205, Exercise 2.23:

• p.205, Exercise 2.25:

• p.205, bottom:

• p.206, top:

• p.207, top:

• p.209, top:

• p.209, middle:

• p.209, before Proposition 3.5:

• p.212, Corollary 3.13:

• p.212, bottom:

• p.214, beginning of section 4.1:

• p.220, Lemma 4.12:

• p.221, top half:

• p.224, middle:

• p.226, Exercise 4.19:

• p.226, Exercise 4.22:

• p.226, footnote:

• p.227, top:

• p.229, Definition 5.6:

• p.232, proof of Proposition 5.11:

• p.232, middle:

• 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 6.8:

• p.241, Exercise 6.10:

• #### Chapter V

• p.244, first paragraph of 1.1:

• p.244, bottom:

• p.245, top half:

• p.246, middle:

• p.247, top:

• p.247, top half:

• p.247, bottom half:

• p.247, bottom half:

• p.250, Exercise 1.7:

• p.250, Exercise 1.9:

• p.250, Exercise 1.12:

• p.250, Exercise 1.13:

• p.251, Exercise 1.17:

• p.255, middle:

• p.256, bottom:

• 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, paragraph preceding the proof:

• p.265, Proof of Proposition 3.5:

• p.267, Exercise 3.13:

• p.267, Exercise 3.15:

• p.269, bottom:

• p.272, middle:

• p.272, diagram:

• p.274, proof of Lemma 4.15:

• p.276, Exercise 4.6:

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

• p.277, bottom:

• p.278, Exercise 4.10:

• p.278, Exercise 4.12:

• p.280, Exercise 4.25:

• 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.290, Exercise 5.22:

• p.292, proof of Lemma 6.2:

• p.292, proof of Lemma 6.3:

• p.295, bottom:

• 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.302, Exercise 6.19:

• p.303, Exercise 6.21:

• #### Chapter VI

• p.308, top:

• p.309-10, proof of Proposition 1.9:

• p.310, bottom:

• p.311, middle:

• p.312, Exercise 1.3:

• p.312, Exercise 1.4:

• p.313, Exercise 1.15:

• p.314, Exercise 1.19:

• p.316, top:

• p.317, footnote:

• p.319, bottom:

• p.326, Exercise 2.10:

• p.328, middle:

• p.329, footnote 17:

• p.333, proof of Proposition 3.7:

• p.334, proof of Claim 3.10:

• p.341, middle:

• p.343, bottom:

• p.347, Exercise 4.6:

• 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.366, Lemma 6.14:

• p.367, bottom:

• p.368, Exercise 6.4:

• p.370, top:

• p.370, Exercise 6.16:

• p.370, Exercise 6.18:

• p.370, footnote:

• p.371, Exercise 6.21:

• p.371, Exercise 6.22:

• p.378, following the proof:

• p.383, Exercise 7.16:

• p.383, Exercise 7.16:

• #### Chapter VII

• p.385, bottom:

• p.386, second paragraph:

• p.387, top:

• p.387, bottom:

• p.388, top half:

• p.389, second paragraph:

• p.389, Proposition 1.5:

• p.391, Definition 1.8:

• p.393, Example 1.12:

• p.393, bottom:

• p.397, Exercise 1.6:

• p.397, Exercise 1.8:

• p.398, Exercise 1.15:

• p.400, Exercise 1.29:

• p.402, proof of Claim 2.5:

• p.403, top:

• p.403, bottom:

• p.404, top:

• p.410, top:

• p.411, top:

• p.414, Exercise 2.6:

• p.416, bottom:

• p.421, proof of Lemma 3.3:

• p.423, bottom:

• p.426, middle:

• p.431, Proof of Theorem 4.8:

• p.436, beginning of 4.3:

• p.439, Exercise 4.8:

• 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.459, top:

• p.464, middle:

• p.465, bottom:

• p.466, Exercise 6.2:

• p.471, bottom:

• p.472, top:

• p.473, end of first paragraph:

• p.474, top:

• p.475, proof of Lemma 7.11:

• p.476, top:

• p.476, Proof of Lemma 7.13:

• p.476-7, Proof of Proposition 7.14:

• p.478, third paragraph:

• p.480, Exercise 7.2:

• p.481, Exercise 7.11:

• #### Chapter VIII

• p.489, top:

• p.490, bottom:

• p.491, second-to-last paragraph:

• p.492, bottom:

• p.495, bottom:

• p.496, Exercise 1.5:

• p.497, Exercise 1.7:

• p.497, Exercise 1.9:

• p.497, Exercise 1.10:

• p.497, Exercise 1.11:

• p.498, Exercise 1.12:

• p.505, Corollary 2.6:

• p.509, bottom half:

• p.521, Exercise 3.9:

• p.522, Exercise 3.15:

• p.525, bottom:

• p.526, top half:

• p.527, top half:

• p.529, (iv)=>(ii):

• p.529, middle:

• p.532, Exercise 4.3:

• p.533, Exercise 4.12:

• p.535, Exercise 4.22:

• p.538, Proof of Proposition 5.5:

• p.540, bottom:

• p.542, top:

• p.542, middle:

• p.543, Exercise 5.3:

• p.544, Exercise 5.9:

• p.544, Exercise 5.12:

• p.544, Exercise 5.13:

• p.545, last line:

• p.546, Lemma 6.2:

• p.547, middle:

• p.549, bottom:

• p.550, Proof of Lemma 6.9:

• p.554, beginning of Section 6.5:

• p.555, first display:

• p.555, Exercise 6.5:

• p.557, Exercise 6.22, last bullet:

• #### Chapter IX

• p.563, Lemma 1.5:

• p.563, bottom:

• p.567, bottom:

• p.568, bottom:

• p.569, middle:

• p.574, Exercise 1.8:

• p.575, top:

• p.575, Exercise 1.14:

• p.578, top:

• p.580, top row of the diagram:

• p.580, bottom half:

• p.582, top:

• p.584, bottom:

• p.591, Exercise 2.17:

• 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.602, Exercise 3.1:

• p.604, footnote:

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

• p.614, top:

• p.614, Exercise 4.5:

• p.629, middle:

• 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.651, bottom:

• p.655, middle:

• p.660, Exercise 7.14:

• p.661, hint to Exercise 7.15:

• p.662, Example 8.2:

• p.663, statement of Theorem 8.3:

• p.663, bottom:

• p.668, Example 8.8:

• p.674, Theorem 8.12, first bullet:

• p.687, middle:

• p.695, Exercise 9.2: