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Displaying similar documents to “Inner Products, Group, Ring of Quaternion Numbers”

Some Operations on Quaternion Numbers

Bo Li, Xiquan Liang, Pan Wang, Yanping Zhuang (2009)

Formalized Mathematics

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In this article, we give some equality and basic theorems about quaternion numbers, and some special operations.

Explicit moduli for curves of genus 2 with real multiplication by ℚ(√5)

John Wilson (2000)

Acta Arithmetica

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1. Motivation. Let J₀(N) denote the Jacobian of the modular curve X₀(N) parametrizing pairs of N-isogenous elliptic curves. The simple factors of J₀(N) have real multiplication, that is to say that the endomorphism ring of a simple factor A contains an order in a totally real number field of degree dim A. We shall sometimes abbreviate "real multiplication" to "RM" and say that A has maximal RM by the totally real field F if A has an action of the full ring of integers of F. We...

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 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.