A characterisation of Gorenstein orders in quarternition algebras.

Brzeziński, Juliusz

doi:10.7146/math.scand.a-11940

Cited by 15 publications

(10 citation statements)

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“…This construction has been attributed to Eichler and appears in Brzezinski [5], in the case R ¼ Z. In this association, the reversal map corresponds to the standard involution on B.…”

Section: Letmentioning

confidence: 93%

Characterizing quaternion rings over an arbitrary base

Voight

2011

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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“…This construction has been attributed to Eichler and appears in Brzezinski [5], in the case R ¼ Z. In this association, the reversal map corresponds to the standard involution on B.…”

Section: Letmentioning

confidence: 93%

Characterizing quaternion rings over an arbitrary base

Voight

2011

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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“…A good reference for this result is Chapter 22 of Voight's book [Voi18]. A correspondence between primitive ternary quadratic forms and Gorenstein orders was established by Brzeziński in [Brz82]. The specific correspondence used here appears in [GL09] and [Voi11].…”

Section: Non-eichler Orders In M 2 (K)mentioning

confidence: 97%

Arithmetical invariants of local quaternion orders

Baeth

Smertnig

2018

Acta Arith.

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Let D be a DVR, let K be its quotient field, and let R be a D-order in a quaternion algebra A over K.and is one of the basic arithmetical invariants that is studied in factorization theory. We characterize finiteness of ρ(R • ) and show that the set of distances ∆(R • ) and all catenary degrees c d (R • ) are finite. In the setting of noncommutative orders in central simple algebras, such results have only been understood for hereditary orders and for a few individual examples.

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“…From here on we assume that p ∤ 2, and we fix δ ∈ O such that ( δ p ) = −1. The correspondence between isomorphism classes of Gorenstein orders in quaternion algebras over local fields and ternary quadratic forms was developed in [Brz82]. This correspondence was explored further in [Lem11], where it is refined to describe Bass orders.…”

Section: Constructing Subordersmentioning

confidence: 99%

Computing ideal classes representatives in quaternion algebras

Pacetti

Sirolli

2014

Math. Comp.

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Let $K$ be a totally real number field and let $B$ be a totally definite quaternion algebra over $K$. In this article, given a set of representatives for ideal classes for a maximal order in $B$, we show how to construct in an efficient way a set of representatives of ideal classes for any Bass order in $B$. The algorithm does not require any knowledge of class numbers, and improves the equivalence checking process by using a simple calculation with global units. As an application, we compute ideal classes representatives for an order of level 30 in an algebra over the real quadratic field $\Q[\sqrt{5}]$.Comment: Corrected version. Section 4 has been rewritten from scratc

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A characterisation of Gorenstein orders in quarternition algebras.

Cited by 15 publications

References 0 publications

Characterizing quaternion rings over an arbitrary base

Characterizing quaternion rings over an arbitrary base

Arithmetical invariants of local quaternion orders

Computing ideal classes representatives in quaternion algebras

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