Regularity of Analytic Algebra of Prime Characteristic |
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Authors: | Mamoru Furuya |
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Institution: | Department of Mathematics, Faculty of Science and Technology , Meijo University , Nagoya , Aichi , Japan |
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Abstract: | Let A be an analytic algebra over a field k of characteristic p > 0. In this article, for an analytic k-algebra we introduce the concept of analytic pn-basis which generalizes the pn-basis defined in 1
Furuya , M. ,
Niitsuma , H. ( 2002 ). Regularity criterion of Noetherian local rings of prime characteristic . J. Algebra 247 : 219 – 230 .Crossref], Web of Science ®] , Google Scholar]], and the concept of an pn-admissible field for an algebraic function field, we give regularity criteria and absolute regularity criteria for an analytic algebra A/k in terms of the higher differential algebra and analytic pn-basis. The results are partial extension of our previous results for affine algebras to the case of analytic algebras (cf. 1
Furuya , M. ,
Niitsuma , H. ( 2002 ). Regularity criterion of Noetherian local rings of prime characteristic . J. Algebra 247 : 219 – 230 .Crossref], Web of Science ®] , Google Scholar], 3
Furuya , M. ,
Niitsuma , H. (2006). Regular local rings essentially of finite type over fields of prime characteristic. J. Algebra 306:703–711.Crossref], Web of Science ®] , Google Scholar]]), and these are partial generalization of results of Orbanz in the analytic case (cf. 9
Orbanz , U. ( 1973 ). Höhere Derivationen und Regularität . J. Reine Angew. Mathematik 262/263 : 194 – 204 .Crossref] , Google Scholar]]). |
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Keywords: | Absolutely regular Analytic algebra Analytic p n -basis Higher differential algebra Module of differentials p n -admissble |
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