The Algebra of Differentials of Infinite Rank

Abstract

Let k and A denote commutative rings with identity and assume that A is a k-algebra. A qth order k-derivation δ of A into an A -module V is an element of Homk(A, V) such that for any q + 1 elements a0, … , aq of A, the following identity holds:Thus, a 1st-order derivation is just an ordinary derivation of A into V.