Summary: ERRATA FOR GRADUATE ALGEBRA: COMMUTATIVE VIEW
Thanks to S. Dahari, M. Schein, and Liu Wanmin.
1. Extra result needed on p. 243
Lemma: If an affine integral domain R is an integral extension of C, then every saturated chain
P · · · P of prime ideals of R intersects down to a saturated chain of prime ideals PC · · · P C
Proof: Passing to R/P and C/(P C), one may assume that P = 0, and it suffices to prove that
if P has height 1, then so does P C. But C is integral over some polynomial ring C , so R is integral
over C . By Going Down (Theorem 6.47), P C has height 1. But this implies P C has height 1.
Also, Exercise 6.8 on page 265 is harder than desirable.
· Page 66 line -9: A has the form
, where (r) = d and
· Page 72 line -3: ¯ = + Fdi
· Page 182 line -8: If A1,