ERRATA Abstract Algebra, Second Edition by D. Dummit and R ...

* page 646, Exercise 10from: Prove that the subring k[x, x 2 y, x 3 y 2 ,...,x i y i−1 ,...] of the polynomial ring k[x, y] isnot afinitely generated k-algebra. (Thus a subalgebra of a finitely generated k-algebra need notbe finitely generated nor Noetherian.)to: Prove that the subring k[x, x 2 y, x 3 y 2 ,...,x i y i−1 ,...] of the polynomial ring k[x, y] isnota Noetherian ring, hence not a finitely generated k-algebra. (Thus subrings of Noetherianrings need not be Noetherian and subalgebras of finitely generated k-algebras need not befinitely generated.)* page 663, Exercise 32, line 2from: ideasto: ideals* page 664, Exercise 41(b), line 3from: ∪ a∈R (0) a = ∪ a∈R rad ((0) a ).]to: ∪ a∈R−{0} (0) a = ∪ a∈R−{0} rad ((0) a ).]* page 665, Exercise 45from: A = rad I.to: A = rad ((F )).* page 665, Exercise 45(f), line 1from: Q ≠ P .to: Q ≠ P, M.* page 665, Definitionfrom: 1 S ∈ R.to: 1=1 S ∈ R.* page 670, line −5from: da 0 ,...,da k−1 ∈ Zto: d k a 0 ,d k−1 a 1 ,...,da k−1 ∈ Z* page 675, end of line 2from: i.e., henceto: i.e.,* page 676, Exercise 10, hintfrom: the conjugates of α areto: the conjugates of α, i.e., the roots of m α,k (x), are* page 676, Exercise 12from: Suppose that S is an integral domain, that R is integrally closed in S, and that P is aprime ideal in R. Let s be any element in the ideal PS generated by P in S.to: Suppose S is an integral domain that is integral over a ring R as in the previous exercise.If P is a prime ideal in R, let s be any element in the ideal PS generated by P in S.* page 692, line −8from: Corollary 10to: Corollary 137