Displaying similar documents to “Some Operations on Quaternion Numbers”

Inner Products, Group, Ring of Quaternion Numbers

Fuguo Ge (2008)

Formalized Mathematics

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In this article, we define the division of the quaternion numbers, we also give the definition of inner products, group, ring of the quaternion numbers, and we prove some of their properties.MML identifier: QUATERN2, version: 7.8.10 4.100.1011

A deceptive fact about functions

Wiesław Dziobiak, Andrzej Ehrenfeucht, Jacqueline Grace, Donald Silberger (2000)

Fundamenta Mathematicae

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The paper provides a proof of a combinatorial result which pertains to the characterization of the set of equations which are solvable in the composition monoid of all partial functions on an infinite set.

Ordered fields and the ultrafilter theorem

R. Berr, Françoise Delon, J. Schmid (1999)

Fundamenta Mathematicae

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We prove that on the basis of ZF the ultrafilter theorem and the theorem of Artin-Schreier are equivalent. The latter says that every formally real field admits a total order.

A factorization theorem for the transfinite kernel dimension of metrizable spaces

M. Charalambous (1998)

Fundamenta Mathematicae

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We prove a factorization theorem for transfinite kernel dimension in the class of metrizable spaces. Our result in conjunction with Pasynkov's technique implies the existence of a universal element in the class of metrizable spaces of given weight and transfinite kernel dimension, a result known from the work of Luxemburg and Olszewski.