On mono-unary algebras corresponding to n-ary groupoids
Rings and Algebras
2018-03-07 v4 Combinatorics
Abstract
In this paper we modify and generalize a construction presented by Novotn\'y: given a groupoid (a set equipped with a binary operation), it is defined a mono-unary algebra corresponding to that specific groupoid. We shall introduce and study a functor from the category of n-ary groupoids to the category of mono-unary algebras. The main result of this paper concerns the construction of homomorphisms between n-ary groupoids, a natural generalization of the method presented by Novotn\'y.
Keywords
Cite
@article{arxiv.1705.00914,
title = {On mono-unary algebras corresponding to n-ary groupoids},
author = {Hilário Fernandes de Araújo Júnior},
journal= {arXiv preprint arXiv:1705.00914},
year = {2018}
}
Comments
The author was notified that the constructions described in the paper were already described in Construction of all homomorphisms of mono-n-ary algebras, Czechoslovak Mathematical Journal, Vol. 46 (1996), No. 2, 331--333