Nicely semiramified division algebras over Henselian fields

Mounirh, Karim

doi:10.1155/ijmms.2005.571

Cited by 4 publications

(1 citation statement)

References 5 publications

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“…In case (4), since D is nicely semiramified, by definition (see[42], p. 149) it contains maximal subfields K and L, with K unramified over F and L totally ramified over F . (In fact, by[75], Th. 2.4, D is nicely semiramified if and only if it has such maximal subfields.)…”

mentioning

confidence: 97%

Multiplicative groups of division rings

Hazrat¹,

Mahdavi-Hezavehi²,

Motiee³

2014

Mathematical Proceedings of the Royal Irish Academy

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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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mentioning

confidence: 97%

Multiplicative groups of division rings

Hazrat¹,

Mahdavi-Hezavehi²,

Motiee³

2014

Mathematical Proceedings of the Royal Irish Academy

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Division Algebras over Henselian Fields

Tignol

Wadsworth

2015

Springer Monographs in Mathematics

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SK1 of graded division algebras

Hazrat

Wadsworth

2011

Isr. J. Math.

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Abstract. The reduced Whitehead group SK 1 of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the ungraded case are then established by the following two theorems: It is proved that SK 1 of a tame valued division algebra over a henselian field coincides with SK 1 of its associated graded division algebra. Furthermore, it is shown that SK 1 of a graded division algebra is isomorphic to SK 1 of its quotient division algebra. The first theorem gives the established formulas for the reduced Whitehead group of certain valued division algebras in a unified manner, whereas the latter theorem covers the stability of reduced Whitehead groups, and also describes SK 1 for generic abelian crossed products.

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Nicely semiramified division algebras over Henselian fields

Cited by 4 publications

References 5 publications

Multiplicative groups of division rings

Multiplicative groups of division rings

Division Algebras over Henselian Fields

SK1 of graded division algebras

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