On a multiplicative structure of BP-cohomology operation algebra (Q808479)

The author studies the multiplicative structure of the ring \(BP^*BP\) of cohomology operations for Brown-Peterson cohomology theory BP at a fixed prime p. His main result is a complicated formula for the composition of two Quillen elements \(r_ E\), analogous to the product formula for the Steenrod algebra given by \textit{J. Milnor} [Ann. Math., II. Ser. 67, 150- 171 (1958; Zbl 0080.380)]. He uses this formula to examine the algebraic structure of the subalgebra of \(BP^*BP\) generated over \(BP^*\) by the Quillen elements.