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A Very Brief Note on Some Commutative Algebraic Properties of a Dirac-Fueter Modified Equation

Daniel Alayon-Solarz
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Abstract

We call attention to the unusual properties that the 4 dimensional solutions for a modified Fueter-Dirac equations satisfy: In a coordinate-free, constant-free and strictly mathematical way it is possible to show that all the solutions for a modified Fueter-Dirac Equation, which are radial symmetric when restricted to the 3-space, have a nice algebraic structure. Locally, these solutions behave naturally in a algebraic way determined by a certain commutative ring related to the quaternions with non-invertibles. This ring has a nontrivial localization. By using left and right versions of the operator we obtain quirality.

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Daniel Alayon-Solarz. 2004-12-06. A Very Brief Note on Some Commutative Algebraic Properties of a Dirac-Fueter Modified Equation. https://arxiv.org/abs/math-ph/0412013

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