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We repair several foolish mistakes concerning tensor products in the paper cited above [2]. I am indebted to (and flattered by) the careful attention paid to these results by Nikolaus Vonessen, who uncovered the errors and suggested corrections. Secondly, we point out the similarity between a theorem about dynamics of actions on a torus due to Mané and a proposition of G. Bergman. Finally, we connect the Faithful Units Conjecture to more traditional versions of the Nullstellensatz. My thanks to Robert Snider for pointing me in the right direction, here. We begin with a more transparent proof of Lemma 14 of [2]. Suppose that H is a commutative F-algebra and k 2 ¿D F is a tower of fields. If / is an ideal of k®FH such that I = k(I n(L®F H)) then

Remarks and corrections for: “Groups acting on affine algebras” [Trans. Amer. Math. Soc. 310 (1988), no. 2, 485–497; MR0940913 (89i:16029)]