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Some properties of the norm in a quaternion division algebra

In this paper we provide some applications of the norm form in some quaternion division algebras over rational field and we give some properties of Fibonacci sequence and Fibonacci sequence in connection with quaternion elements. We define a monoid structure over a fnite set on which we will prove that the defined Fibonacci sequence is stationary, we provide some properties of the norm of a rational quaternion algebra, in connection to the famous Lagrange's four-square theorem and its generalizations given by Ramanujan. Moreover, we prove some results regarding the arithmetic of integer quaternions defined on some division quaternion algebras and we define and give properties of some special quaternions by using Fibonacci sequences.

preprint2020arXivOpen access
Cristina FlautDiana Savin
math.RA
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Open access2 authors1 topic
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Cristina FlautDiana Savin

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