A sequence of ideals Ik,n ⊆ BP* is introduced, with the property: Ik,n ⊆ Ann(γk,n), where γk,n is the toral class of the Brown-Peterson homology of the n-fold product BZ/pk × ··· × BZ/pk. These ideals seem to play an interesting and yet unclear role in understanding Ann(γk,n). They are defined by using the formal group law of the Brown-Peterson spectrum BP, and some of their elementary properties are established. By using classical theorems of Landweber and of Ravenel-Wilson, the author computes the radicals of Ik,n and Ann(γk,n), and discusses a few examples.
