#### Document Type

Article

#### Abstract

The bordism ring *MU*∗(*CP*^{∞}) is central to the theory of formal groups as applied by D. Quillen, J. F. Adams, and others recently to complex cobordism. In the present paper, rings *E*∗(*CP*^{∞}) are considered, where *E* is an oriented ring spectrum, *R*=π∗(*E*), and *pR*=0 for a prime *p*. It is known that *E*∗(*CP*^{∞}) is freely generated as an *R*-module by elements {*β*_{τ}|*r*≧0}. The ring structure, however, is not known. It is shown that the elements {*β*_{pτ}|*r*≧0} form a simple system of generators for *E*∗(*CP*^{∞}) and that *β*_{pτ}^{p}≡*s*^{pτ}*β*_{pτ} mod(*β*₁,⋯,*β*_{pτ-1}) for an element *s* ∈ *R* (which corresponds to [*CP*^{p-1}] when *E*=*MUZ*_{p}). This may lead to information concerning *E*∗(*K*(*Z*,*n*)).

#### Disciplines

Mathematics

#### Recommended Citation

C. Schochet, On the bordism ring of complex projective space, *Proceedings of the American Mathematical Society* **37(1)** (1973), 267-270.

## Comments

First published in the

Proceedings of the American Mathematical Society37(1)(1973, http://dx.doi.org/10.1090/S0002-9939-1973-0307222-2), published by the American Mathematical Society.