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We consider the polynomial algebra      H ∗  ( C P ∞  ×  C P ∞  ; F p ) H^*(\mathbf {C} P^\infty \times \mathbf {C} P^\infty ; \mathbf {F}_p)       as a module over the mod      p p       Steenrod algebra,      A ( p ) \mathcal {A}(p)      ,      p p       being an odd prime. We give a minimal set of generators consisting of monomials and characterise all such ‘monomial bases’.

Monomial Bases for 𝐻*(𝐂𝐏^{∞}×𝐂𝐏^{∞}) over 𝒜(𝓅)