QDA

(redirected from Quaternion Division Algebra)
AcronymDefinition
QDAQualitative Data Analysis
QDAQuality of Everyday Activities (cancer survey factor)
QDAQuetta Development Authority (Balochistan, Pakistan)
QDAQuantitative Descriptive Analysis (statistics)
QDAQuantitative Data Analysis
QDAQuantity Discount Agreement
QDAQuick Defect Analysis
QDAQuaternion Division Algebra
QDAQuadratic Discriminate Analysis
QDAQualified Dental Assistant
QDAQuestionnaire-Diagnosed Asthma
References in periodicals archive ?
[not equal to] 2, a quaternion division algebra D with the standard involution J over k such that D is defined over a global field L, and D [cross product] [K.sub.v] is not trivial for at least four places v of K for any finite subextension L [subset] K [subset] k.
2) For such a field k and quaternion division algebra D, there are skew-hermitian forms h (resp.
Kaplansky showed in [1] that Q is the unique quaternion division algebra over K if and only if
Tsukamoto [10] obtained a classification for skew-hermitian forms over the unique quaternion division algebra over a field K that is either real closed or a local number field.
Let K be a Kaplansky field and let Q be the unique quaternion division algebra over K.
Then [(a, d).sub.K] is a quaternion division algebra and not isomorphic to Q, contradicting the hypothesis.
To show its necessity, suppose that Q is not the unique quaternion division algebra over K.
Let K be a nonreal Kaplansky field and let Q be the unique quaternion division algebra over K.
If K is euclidean, then [(-1, - 1).sub.K] is the unique quaternion division algebra over K, in particular K is a Kaplansky field.
Let Q be a quaternion division algebra over afield K with norm form [N.sub.Q].