Structural analysis of Pythagorean monoids

Abstract

This article reports on studies of the structure of a monoid that consists of all linear transformations which map Pythagorean triples into Pythagorean triples. A detailed description of the elements of the monoid with all LPTs whose rank is 1, is given. An open problem is discussed and a partial answer given. The results of this analysis will be of interest to a broad spectrum of readers. It bridges such concepts as fixed point, linear transformation, and Pythagorean triple. It should be of pedagogical as well as theoretical value.

Acknowledgements

The authors wish to take this opportunity to thank the Referencing/Reviewing Committee for their valuable suggestions and comments.