Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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

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).


References [Enhancements On Off] (What's this?)

  • [1] M. Auslander and O. Goldman, Maximal orders, Trans. Amer. Math. Soc. 97 (1960), 1-24. MR 22 #8034. MR 0117252 (22:8034)
  • [2] A. Brumer, Structure of hereditary orders, Thesis, Princeton University, Princeton, N. J., 1963; cf. Bull. Amer. Math. Soc. 69 (1963), 721-724; addendum, ibid. 70 (1964), 185. MR 28 #115. MR 0152565 (27:2543)
  • [3] M. Deuring, Algebren, Springer, Berlin, 1934. MR 0228526 (37:4106)
  • [4] M. Harada, Hereditary orders, Trans. Amer. Math. Soc. 107 (1963), 273-290. MR 27 #1474. MR 0151489 (27:1474)
  • [5] H. Jacobinski, Genera and decompositions of lattices over orders, Acta Math. 121 (1968), 1-29. MR 0251063 (40:4294)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16.20

Retrieve articles in all journals with MSC: 16.20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0272807-7
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

American Mathematical Society