Fiberings with Fiber RP(k)

Let k be non–negative integer. The unoriented bordism classes, which can be represented as RP(ξ ^k )] where ξ ^k is a k–plane bundle, form an ideal of the unoriented bordism ring MO_*. A group of generators of this ideal expressed by a base of MO_* and a necessary and sufficient condition for a bordism class to belong to this ideal are given. This work is supported by HNSF (Grant No: 103144) and NNSF of China (10371029)