Multiplicative groups of division rings

Roozbeh Hazrat; M. Mahdavi-Hezavehi; M. Motiee

doi:10.3318/PRIA.2014.114.04

Multiplicative groups of division rings

Roozbeh Hazrat, M. Mahdavi-Hezavehi, M. Motiee

Research output: Contribution to journal › Article

Abstract

Exactly 170 years ago, the construction of the real quaternion algebra by William Hamilton was announced in the Proceedings of the Royal Irish Academy. It became the first example of non-commutative division rings and a major turning point of algebra. To this day, the multiplicative group structure of quaternion algebras have not completely been understood. This article is a long survey of the recent developments on the multiplicative group structure of division rings.

Original language	English
Pages (from-to)	37-114
Number of pages	78
Journal	Mathematical Proceedings of Royal Irish Academy
Volume	114
Issue number	1
DOIs	https://doi.org/10.3318/PRIA.2014.114.04
Publication status	Published - 2014

Keywords

algebra
noncommutative algebras

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10.3318/PRIA.2014.114.04

http://arxiv.org/abs/1302.0596

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title = "Multiplicative groups of division rings",

abstract = "Exactly 170 years ago, the construction of the real quaternion algebra by William Hamilton was announced in the Proceedings of the Royal Irish Academy. It became the first example of non-commutative division rings and a major turning point of algebra. To this day, the multiplicative group structure of quaternion algebras have not completely been understood. This article is a long survey of the recent developments on the multiplicative group structure of division rings.",

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AB - Exactly 170 years ago, the construction of the real quaternion algebra by William Hamilton was announced in the Proceedings of the Royal Irish Academy. It became the first example of non-commutative division rings and a major turning point of algebra. To this day, the multiplicative group structure of quaternion algebras have not completely been understood. This article is a long survey of the recent developments on the multiplicative group structure of division rings.

KW - algebra

KW - noncommutative algebras

UR - http://handle.uws.edu.au:8081/1959.7/uws:29155

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DO - 10.3318/PRIA.2014.114.04

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JO - Mathematical Proceedings of Royal Irish Academy

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Multiplicative groups of division rings

Abstract

Keywords

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