The Algebraic EHP Sequence

Let be the dual of the Steenrod algebra. If , are graded unstable -comodules, one can define and compute the derived functors <!-- MATH ${\text{Coext} _A}(M,N)$ --> using unstable injective resolutions of . Bousfield and Curtis have shown that these unstable Coext groups can be fit into a long exact ``EHP sequence", an algebraic analogue of the EHP sequence of homotopy theory. Our object in the present paper is to study the relationship between the , and homomorphisms and the composition pairing <!-- MATH ${\text{Coext} _A}(N,R) \otimes {\text{Coext} _A}(M,N) \to {\text{Coext} _A}(M,R)$ --> . Among our results is a formula that measures the failure of the composition product to commute.