Groups and monoids of Pythagorean triples connected to conics

Nadir Murru; Marco Abrate; Stefano Barbero; Umberto Cerruti

Open Mathematics (2017)

  • Volume: 15, Issue: 1, page 1323-1331
  • ISSN: 2391-5455

Abstract

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We define operations that give the set of all Pythagorean triples a structure of commutative monoid. In particular, we define these operations by using injections between integer triples and 3 × 3 matrices. Firstly, we completely characterize these injections that yield commutative monoids of integer triples. Secondly, we determine commutative monoids of Pythagorean triples characterizing some Pythagorean triple preserving matrices. Moreover, this study offers unexpectedly an original connection with groups over conics. Using this connection, we determine groups composed by Pythagorean triples with the studied operations.

How to cite

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Nadir Murru, et al. "Groups and monoids of Pythagorean triples connected to conics." Open Mathematics 15.1 (2017): 1323-1331. <http://eudml.org/doc/288279>.

@article{NadirMurru2017,
abstract = {We define operations that give the set of all Pythagorean triples a structure of commutative monoid. In particular, we define these operations by using injections between integer triples and 3 × 3 matrices. Firstly, we completely characterize these injections that yield commutative monoids of integer triples. Secondly, we determine commutative monoids of Pythagorean triples characterizing some Pythagorean triple preserving matrices. Moreover, this study offers unexpectedly an original connection with groups over conics. Using this connection, we determine groups composed by Pythagorean triples with the studied operations.},
author = {Nadir Murru, Marco Abrate, Stefano Barbero, Umberto Cerruti},
journal = {Open Mathematics},
keywords = {Conics; Pythagorean groups; Pythagorean monoids; Pythagorean triples; Pythagorean triple preserving matrices},
language = {eng},
number = {1},
pages = {1323-1331},
title = {Groups and monoids of Pythagorean triples connected to conics},
url = {http://eudml.org/doc/288279},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Nadir Murru
AU - Marco Abrate
AU - Stefano Barbero
AU - Umberto Cerruti
TI - Groups and monoids of Pythagorean triples connected to conics
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 1323
EP - 1331
AB - We define operations that give the set of all Pythagorean triples a structure of commutative monoid. In particular, we define these operations by using injections between integer triples and 3 × 3 matrices. Firstly, we completely characterize these injections that yield commutative monoids of integer triples. Secondly, we determine commutative monoids of Pythagorean triples characterizing some Pythagorean triple preserving matrices. Moreover, this study offers unexpectedly an original connection with groups over conics. Using this connection, we determine groups composed by Pythagorean triples with the studied operations.
LA - eng
KW - Conics; Pythagorean groups; Pythagorean monoids; Pythagorean triples; Pythagorean triple preserving matrices
UR - http://eudml.org/doc/288279
ER -

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