Primitive Generators for Algebras
LetHbe a graded commutative algebra with a nice set of algebra generators. LetHalso be a comodule over a Hopf algebraA. In Section 2 we give conditions under which certain of these generators ofHcan be rechosen to be primitive. In addition we give explicit formulas expressing these primitive generators in terms of the original set of generators.In Section 3 we apply the theory of Section 2 to the modphomology of the Thorn spectraMO, MUandMSp.In particular we give two explicit descriptions of the image of the Hurewicz homomorphism forMO.One of these makes explicit the recursive computation of E. Brown and F. Peterson [1].In Section 4 we give a variation of the theory of Section 2 which computes primitive generators of certain Hopf algebras. This theory is applied to study the primitive elements ofH*(BU)andH*(SO;Z2).