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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
MathSciNet review: 0272807
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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).

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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