On the generators of the polynomial algebra as a module over the Steenrod algebra

摘要

Let P-k := F-2 [x(1). x(2), ..., x(k)] be the polynomial algebra over the prime field of two elements, F-2, in k variables x(1), x(2), ..., x(k), each of degree 1. We are interested in the Peterson hit problem of finding a minimal set of generators for Pk as a module over the mod-2 Steenrod algebra, A. In this paper, we study the hit problem in degree (k - 1)(2(d) - 1), with d a positive integer. Our result implies the one of Mothebe [4,5]. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.