Groups and monoids of Pythagorean triples connected to conics

• Autorzy: Nadir Murru , Marco Abrate , Stefano Barbero , Umberto Cerruti
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Conics; Pythagorean groups; Pythagorean monoids; Pythagorean triples; Pythagorean triple preserving matrices

Kategorie tematyczne

• 11A99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 1323-1331

Daty

wydano

2017-11-01

otrzymano

2017-08-11

zaakceptowano

2017-09-22

online

2017-11-10

Twórcy

autor

Nadir Murru

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autor

Marco Abrate

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autor

Stefano Barbero

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autor

Umberto Cerruti

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Identyfikatory

DOI

10.1515/math-2017-0111