A note on -bases of rings

Author:
Tomoaki Ono

Journal:
Proc. Amer. Math. Soc. **128** (2000), 353-360

MSC (1991):
Primary 13N05; Secondary 13B05

DOI:
https://doi.org/10.1090/S0002-9939-99-05029-7

Published electronically:
July 6, 1999

MathSciNet review:
1623048

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a tower of rings of characteristic . Suppose that is a finitely presented -module. We give necessary and sufficient conditions for the existence of -bases of over . Next, let be a polynomial ring where is a perfect field of characteristic , and let be a regular noetherian subring of containing such that . Suppose that is a free -module. Then, applying the above result to a tower of rings, we shall show that a polynomial of minimal degree in is a -basis of over .

**1.**T. Kimura and H. Niitsuma,*On Kunz's conjecture*, J. Math. Soc. Japan**34**(1982), 371-378. MR**83h:13030****2.**-,*A note on -basis of polynomial ring in two variable*, SUT J. Math.**25**(1989), 33-38. MR**91a:13002****3.**E. Kunz,*Kähler Differentials*, Vieweg Advanced Lectures in Math., 1986. MR**88e:14025****4.**H. Matsumura,*Commutative Ring Theory*, Cambridge University Press, Cambridge, 1986. MR**88h:13001****5.**D. Quillen,*Projective modules over polynomial rings*, Invent. Math.**36**(1976), 167-171. MR**55:337****6.**S. Yuan,*Inseparable Galois theory of exponent one*, Trans. Amer. Math. Soc.**149**(1970), 163-170. MR**41:1717**

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Additional Information

**Tomoaki Ono**

Affiliation:
Tokyo Metropolitan College of Aeronautical Engineering 8-52-1, Minami-senju, Arakawa-ku, Tokyo 116-0003, Japan

Email:
tono@kouku-k.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-99-05029-7

Keywords:
$p$-basis,
derivation,
Galois extension

Received by editor(s):
January 19, 1998

Received by editor(s) in revised form:
April 1, 1998

Published electronically:
July 6, 1999

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1999
American Mathematical Society