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arXiv · 2306.12429

On semi-Peano algebras

Carles Cardó
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Abstract

A semi-Peano algebra is an algebra for which each operation is injective, and the images of the operations are pairwise disjoint. The most straightforward non-trivial kind of finitely presented semi-Peano algebra are algebras with a single unary operation. There are two possible directions of generalization: algebras with a single operation of any arity, and algebras with several unary operations. The former can be solved easily by adapting results on equidecomposable groupoids from [2]. However, the second way is somewhat different. We will show that a finitely presented multi-unary semi-Peano algebra is the free product of cyclic semi-Peano algebras and that a unique relation defines such cyclic algebras. In addition, we will characterize each cyclic algebra up to isomorphism.

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Carles Cardó. 2023-06-01. On semi-Peano algebras. https://arxiv.org/abs/2306.12429

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