Counting non-isomorphic generalized Hamilton quaternions

DOI10.24330/ieja.1058426OpenAlexW4205810847MaRDI QIDQ5034893

José María Grau, Antonio M. Oller-Marcén, Celino Miguel

Publication date: 21 February 2022

Published in: International Electronic Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.24330/ieja.1058426

zbMATH Keywords

quaternion algebrafinite local ringHensel lemma

Mathematics Subject Classification ID

Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Finite commutative rings (13M99)

Cites Work

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• On the structure of quaternion rings over \(\mathbb{Z}/n\mathbb{Z}\)
• On cubic rings and quaternion rings
• On non-commutative quadratic extensions of a commutative ring
• Quadratic algebras, Clifford algebras, and arithmetic Witt groups
• Quaternion algebras over commutative rings
• A general Hensel's lemma
• Generalized quaternion rings over \(\mathbb {Z}/n\mathbb {Z}\) for an odd \(n\)
• About special elements in quaternion algebras over finite fields
• Characterizing quaternion rings over an arbitrary base
• Identifying the Matrix Ring: Algorithms for Quaternion Algebras and Quadratic Forms

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