Annihilator ideals and primitive elements in complex bordism

Abstract

We determine the prime ideals in the complex bordism ring $\pi_{\ast}(MU)$ which can be the annihilator ideals of elements in the complex bordism of finite complexes. Such a prime ideal must be finitely generated and invariant under all stable $MU$-cohomology operations. We go on to determine the invariant prime ideals in $\pi_{\ast}(MU)$.