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 cohomology operations‎, ‎denoted by sq^n‎, ‎between the cohomology groups with z2 coefficients 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 define 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 defining a new linear ordering on the pairs (s+t,s) of exponents of the atomic squares sq^2s(2^t−1) for the integers s≥0 and t≥1‎.