A note on the new basis in the mod 2 Steenrod algebra

The Mod 2 Steenrod algebra is a Hopf algebra that consists of the primary co- homology operations, denoted by Sqn, between the cohomology groups with Z2 coeffcients of any topological space. Regarding to its vector space structure over Z2, it has many base systems and some of the base systems can also be restricted to its sub algebras. On the contrary, in addition to the work of Wood, in this paper we dene a new base system for the Hopf subalgebras A(n) of the mod 2 Steenrod algebra which can be extended to the entire algebra. The new base system is obtained by dening a new linear ordering on the pairs (s + t; s) of exponents of the atomic squares Sq2s(2t_1) for the integers s ⩾ 0 and t ⩾ 1.