1. Regularity of Noetherian local rings
- Author
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Furuya, Mamoru and Niitsuma, Hiroshi
- Subjects
- *
COMMUTATIVE rings , *LOCAL rings (Algebra) , *DIFFERENTIAL algebra , *MATHEMATICS - Abstract
Let
(R,m) be a Noetherian local ring of prime characteristicp . In this paper, as an extension of the concept ofpn -basis, we introduce the notion ofm -adicpn -basis, and we show thatR/Rpn has anm -adicpn -basis for everyn (n=1,2,…) if and only ifR is a regular local ring. For any Noetherian local ring, further we introduce the concept ofm -adic free graded algebra and we give a regularity criterion in terms of the higher differential algebra, and others. [Copyright &y& Elsevier]- Published
- 2004
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