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On Ramification Theory in Projective Orders, II

Published online by Cambridge University Press:  22 January 2016

Shizuo Endo*
Affiliation:
McMaster University and Tokyo University of Education
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Let R be a commutative ring and K be the total quotient ring of R. Let Σ be a separable K-algebra which is a finitely generated projective, faithful K-module and Λ be an R-order in DΛ/R. We denote by DΛ/R the Dedekind different of Λ and by NΛ/R the Noetherian different of Λ.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Auslander, M. and Buchsbaum, D.A., On ramification theory in Noetherian rings, Amer. J. Math., 81 (1959), 749765.CrossRefGoogle Scholar
[2] Endo, S., On ramification theory in projective orders, Nagoya Math. J., 36 (1969); 121141.CrossRefGoogle Scholar
[3] Endo, S. and Watanabe, Y., On separable algebras over a commutative ring, Osaka J. Math., 4 (1967), 233242.Google Scholar
[4] Fossum, R., The Noetherian different of projective orders, J. reine angew. Math., 224 (1966), 209218.Google Scholar
[5] Higman, D.G., On orders in separable algebras, Canadian J. Math., 7 (1955), 509515.Google Scholar
[6] Janusz, G., Separable algebras over commutative rings, Trans. A.M.S., 122 (1966), 461479.CrossRefGoogle Scholar
[7] Nagata, M., Local rings, Interscience Publ., New York, 1962.Google Scholar
[8] Watanabe, Y., The Dedekind different and the homological different, Osaka J. Math., 4 (1967), 227231.Google Scholar