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A note on $p$-bases of rings

1999
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Proceedings of the American Mathematical Society
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Let R ⊇ R ⊇ R p be a tower of rings of characteristic p > 0. Suppose that R is a finitely presented R -module. We give necessary and sufficient conditions for the existence of p-bases of R over R . Next, let A be a polynomial ring k[X 1 , . . . , Xn] where k is a perfect field of characteristic p > 0, and let B be a regular noetherian subring of A containing A p such that [Q(B) : Q(A p )] = p. Suppose that Der A p (B) is a free B-module. Then, applying the above result to a tower B ⊇ A p ⊇ B p

doi:10.1090/s0002-9939-99-05029-7
fatcat:edpjgxhumfgq7kuab7jrt4pkpq