# Errata

### A Field guide to algebra, Undergraduate texts in mathematics, Springer-Verlag, 2004, doi:10.1007/b138364, ISBN:978-0-387-21428-3Algèbre corporelle, Presses de l'École polytechnique, 2005. ISBN:978-2-7302-1217-5

• Example 5.8.8, page 136 and Exemple 5.8.8, page 128.
Of course, the least common multiple of 2, 3, and 5, is equal to 30, and not to 60 as incorrectly written. One thus needs an additional argument to conclude that the Galois group of the indicated polynomial is equal to $\mathfrak A_5$. However, conjugating a double transposition by a 5-cycle, gives a different double transposition, so that this group contains at least two elements of order 2. Its cardinality is thus divisible by 4.

### (Mostly) commutative algebra, Universitext, 2021. doi:10.1007/978-3-030-61595-6, ISBN:978-3-030-61595-6

• The first sentence of statement of corollary 6.5.13 should read: “Let $A$ be a ring and let $M$ be a noetherian $A$-module.” In the proof, when I invoke corollary 6.5.13, one should of course read “proposition 6.5.12”. [12 february 2023]
• The given proof of theorem 9.5.2 (Seidenberg's Going-down theorem). makes use of proposition 9.5.1 which requires the extension $E\to F$ to be finite. Therefore, one should add to the hypothesis of theorem 9.5.2 that the fraction field of $B$ is a finite extension of the fraction field of $A$. (This would hold, in particular, if $B$ is finitely generated over $A$ but that hypothesis is more difficult to check.) See Bourbaki, Algèbre commutative, V, p. 46, prop. 6 for the general case. [E. Kowalski, 17 november 2021]

### Théorie de l'information — Trois théorèmes de Claude Shannon, Calvage & Mounet, 2022

Voir l'erratum ci-joint (12 septembre 2022).

Antoine Chambert-Loir