Dear Jim, Do you know to whom the following theorem should be attributed? If H is a cocommutative, connected (i.e., pointed and irreducible) Hopf algebra over a field K of char. 0, then H is isom. to the universal enveloping algebra of the Lie algebra of primitives P(H). Milnor and Moore prove this for H graded, is this more general result due to Kostant? Or is Kostant's theorem the statement that a general cocommutative H is a product of a univ. env. algebra and a group algebra? Milnor and Moore also extend this to the case when char K=p. Do you know of any extension for K a general commutative ring with unit? I think the theorem holds for K a comm. ring exactly as stated above except with the following added condition on H: Let I be the identity map and 1 be the convolution identity in the convolution algebra of all linear maps Hom(H,H). Then for all n>0, and all x in H, (I-1)^{n}(x) is divisible by n in H. I've proved this for H also commutative, but would like to know if it would be an interesting extension of the above result (or if it's already been done) before trying to prove it in general. I greatly appreciate any help you can give. Yours, Bill =====================================================================