Two remarks about hereditary orders
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- by H. Jacobinski PDF
- Proc. Amer. Math. Soc. 28 (1971), 1-8 Request permission
Abstract:
In the first remark it is shown that, over a Dedekind ring, hereditary orders in a separable algebra are precisely the “maximal” orders under a relation stronger than inclusion (Theorem 1). At the same time simple proofs for known structure theorems of hereditary orders are obtained. In the second remark a complete classification is given of lattices over a hereditary order, provided the underlying Dedekind ring is contained in an algebraic number field and the lattices satisfy the Eichler condition (Theorem 2).References
- Maurice Auslander and Oscar Goldman, Maximal orders, Trans. Amer. Math. Soc. 97 (1960), 1–24. MR 117252, DOI 10.1090/S0002-9947-1960-0117252-7
- Armand Brumer, Structure of hereditary orders, Bull. Amer. Math. Soc. 69 (1963), 721–724. MR 152565, DOI 10.1090/S0002-9904-1963-11002-2
- Max Deuring, Algebren, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 41, Springer-Verlag, Berlin-New York, 1968 (German). Zweite, korrigierte auflage. MR 0228526
- Manabu Harada, Hereditary orders, Trans. Amer. Math. Soc. 107 (1963), 273–290. MR 151489, DOI 10.1090/S0002-9947-1963-0151489-9
- H. Jacobinski, Genera and decompositions of lattices over orders, Acta Math. 121 (1968), 1–29. MR 251063, DOI 10.1007/BF02391907
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 1-8
- MSC: Primary 16.20
- DOI: https://doi.org/10.1090/S0002-9939-1971-0272807-7
- MathSciNet review: 0272807