A convenient basis for a graded ring (Q1924673)

Let \(T\) be the graded polynomial ring \(\mathbb{Z}[e,t_1,t_2,t_3,\dots]\), where \(e\) has degree 2 and \(t_n\) has degree \(2n\). Let \(I\) be the graded ideal of \(T\) generated by the homogeneous relations \(et_n=\sum_{i+j=n+1}t_it_j\) where \(i\) and \(j\) run from 0 to \(n+1\) and \(t_0\) is 1. The paper deals with the structure of the quotient ring \(T/I\). This ring is encountered in algebraic topology. New ring generators \((a_n)_{n\geq 1}\) are defined, possessing simple computational properties, and an additive basis is exhibited in each degree.