Groupoids with Schroder Identity of Generalised Associativity
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2022-12-30 18:04
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PUSHKASHU, D. I.. Groupoids with Schroder Identity of Generalised Associativity. In: Conference of Mathematical Society of the Republic of Moldova, 19-23 august 2014, Chișinău. Chișinău: "VALINEX" SRL, 2014, 3, pp. 154-157. ISBN 978-9975-68-244-2.
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Conference of Mathematical Society of the Republic of Moldova
3, 2014
Conferința "Conference of Mathematical Society of the Republic of Moldova"
Chișinău, Moldova, 19-23 august 2014

Groupoids with Schroder Identity of Generalised Associativity

Pag. 154-157

Pushkashu D. I.
 
Institute of Mathematics and Computer Science ASM
 
Disponibil în IBN: 9 octombrie 2017


Rezumat

We study groupoids that are close to quasigroups with the following SchrÄoder identity (x ¢ y) ¢ (y ¢ (z ¢ x)) = z of generalised associativity. It is proved that if a left cancellation (left division) groupoid (Q; ¢; n) satis¯es this identity and the identity xnx = yny, then (Q; ¢) is a group of exponent two. The similar results are proved for the right case.

Cuvinte-cheie
Groupoid, quasigroup, abelian group,

left (right) division groupoid, left (right) cancellative groupoid,

Schroder identity