## ERRATA

Exercise 1.17 (2): Show that a = < f > with f idempotent.

Proof of Proposition 2.8: Should start with the sentence "Let p = phi^(-1)(q)".

Proposition 3.2: remove "\in rad(R)" after "u-xy".

Exercise 3.17 (3): the notation V(a) has not been introduced yet. It is the set of all prime ideals of R containing the ideal a. See pg. 77, (13.1).

pg. 21, line 9: equals sign between alpha((x_lambda)) and alpha(sum x_lambda e_lambda)

pg 35, line -8: replace F(1_A) by 1_F(A) for consistency (they are equal by (2) in the definition of functor).

pg 51, first line of Thm 8.18 (Watts): the definition of linear functor is on pg 54 (9.2.1), and should be moved before the statement of this theorem.

pg 71, last line of Cor 11.31: at the end it should say p = phi^(-1)( p R'[X]). (The equals sign is missing.)

pg 82, line 13: Set gamma := sum_i x_i s_i phi_i should be gamma := sum_i x_i s_i psi_i = sum_i x_i phi_i.

pg 85, line -4: Given y in pR'_q' intersect R. In addition we assume y nonzero.

pg 87, (14.16) If R is a domain, then this definition recovers that in (10.30), owing to (11.32). A bit more elaboration: if R is integrally closed, then R_p is int closed for all p, since localization commutes with normalization. Conversely, if R' is the integral closure of R, then R'/R localized at every prime is 0, so it's the zero module.

pg 102. The last sentence of the proof of Prop 17.10 should be moved to just before "So b \in p by ...".

pg 113, next display after (19.3.3): there should be an = sign between (M_(i-1))_p/(M_i)_p and the split into cases.

pg 114, line -13: "But a = (x)". Insert "is finitely generated".

pg 114, line -4: Replace 13.26 by (13.27)(3).