Regular local rings essentially of finite type over fields of prime characteristic

[摘要] Let R be a local ring essentially of finite type over a field k of characteristic p > 0. In the paper [M. Furuya, H. Niitsuma, Regularity criterion of Noetherian local rings of prime characteristic, J. Algebra 247 (2002) 219-230], we constructed some regularity criterion for such a local ring R in terms of the higher differential algebra and the p(n)-basis. In this paper, we introduce the concept of a reduced index of a Noetherian ring and we show the sharpened result of the above criterion and further we also give a geometric regularity criterion in terms of the higher differential algebra and the p(n)-basis. The latter criterion yield the sharpened result of a part of Orbanz's theorem [U. Orbanz, Hohere Derivationen and Regularitat, J. Reine. Angew. Math. 262/263 (1973) 194-204, 4.2]. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] regular local ring;p(n)-basis;n-admissible;m-adic higher differential algebra;reduced index