﻿A list of errata in the notes "Introduction to Abstract Algebra" by Samir Siksek ( https://homepages.warwick.ac.uk/staff/S.Siksek/teaching/aa/aanotes.pdf ) in the version of 2015-11-02: [!!! UPDATE !!! This list is no longer up-to-date. To my knowledge, they have all been corrected on 2019-10-18.] - page 5, the displayed equation at the end: Is it a British standard to write decimal points as $\cdots$ instead of $.$s? I'd find it a bit confusing if I didn't already know what you mean. - page 10, Example III.7: This is not obvious (see https://proofwiki.org/wiki/General_Associativity_Theorem ). While the structure of your notes makes it hard to include a proof at this point, a reference to a proof or a proof in an appendix would be highly helpful. - page 24, footnote 1: "if an only if" -> "if and only if". - page 32: "effect $\rho_0$" -> "effect as $\rho_0$". - page 38, §VI.I: Again you are using general associativity (Example III.7) here. - page 40, §VI.2: I'd point out that part of additive notation is writing $a/b$ as $a-b$. - page 43, footnote 1: "where $0 \leq 0 < m$" -> "where $0 \leq a < m$". - page 43, footnote 1: "the observe" -> "then observe". - page 67: In the middle of the page, "\{..., -2k, -k, 0, k, 2k\}$" is missing an "..." at the end. - page 76, Example XII.13: "lets" -> "let's". - page 82, Example XIII.2: I'd put a question mark after "What happens to$f(\theta)$as$\theta$changes", unless you intend to convey that it is a boring question. - page 86, Exercise XIII.12: "of orders$3$" -> "of order$3$". - page 87, proof of Lemma XIII.16: "as it a sum" -> "as it is a sum". - page 96, §XIV.5: No need to require$n \geq 2$in this discussion. - page 98: "product of two permutation" -> "product of two permutations". - page 98: "and example" -> "an example". - page 98, Example XIV.24: "are repeatedly apply" -> "and repeatedly apply". - page 98, Example XIV.24: "as either of" -> "in either of". - page 102, §XIV.8: "the define" -> "then define". - page 105, Example XIV.39: "of$4$transposition" -> "of$4$transpositions". - page 108: "number moves" -> "number of moves". - page 112: Theorem XV.8 is false the way you defined subrings. Indeed, you have not required a subring to have the same unity as the ring (just to have *some* unity); thus, a factor of a direct product of two nontrivial rings is a subring of the direct product, but fails condition (a) of Theorem XV.8. - page 112, Example XV.10: "has an subrings" -> "has a subring different from itself". - page 113, Example XV.12: "subring" -> "a subring" (on the last line of the example). - page 114, Example XV.19: "there some" -> "there is some". - page 116, Example XV.24: Remove the comma after "Although". - page 121, proof of Theorem XVII.2: "is unit" -> "is a unit". - page 121, proof of Theorem XVII.2: "$ab+km$->$ab-km$". - page 123, §XVII.3: Capitalize the "we" on the first line of this section. Also, require$m \geq 1$(or rather$m \geq 2$, since you forbid trivial rings; you might then need to "manually" set$\varphi(1) = 1\$).