An algebraic generalization of image $J$

Abstract

As is well known, the image of the $J$-homomorphism in the stable homotopy groups of spheres is described in terms of the first line of the Adams-Novikov $E_2$-term. In this paper we consider an algebraic analogue of the image of $J$ using the spectrum $T(m)_(j)$ defined by Ravenel and determine the Adams-Novikov first line for small values of $j$.