Two remarks about hereditary orders
Author:
H. Jacobinski
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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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).
- Maurice Auslander and Oscar Goldman, Maximal orders, Trans. Amer. Math. Soc. 97 (1960), 1–24. MR 117252, DOI https://doi.org/10.1090/S0002-9947-1960-0117252-7
- Armand Brumer, Structure of hereditary orders, Bull. Amer. Math. Soc. 69 (1963), 721–724. MR 152565, DOI https://doi.org/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 https://doi.org/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 https://doi.org/10.1007/BF02391907
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16.20
Retrieve articles in all journals with MSC: 16.20
Additional Information
Keywords:
Maximal orders,
hereditary orders,
lattices over hereditary orders,
intersection of maximal orders,
endomorphism ring of the radical,
genera of lattices,
restricted genera
Article copyright:
© Copyright 1971
American Mathematical Society