A note on $p$-bases of rings

Tomoaki Ono
1999 Proceedings of the American Mathematical Society  
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
more » ... f rings, we shall show that a polynomial of minimal degree in B − A p is a p-basis of B over A p .
doi:10.1090/s0002-9939-99-05029-7 fatcat:edpjgxhumfgq7kuab7jrt4pkpq