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Effective codescent morphisms of $n$-quasigroups and $n$-loops

Dali Zangurashvili

Abstract

Effective codescent morphisms of $n$-quasigroups and of $n$-loops are characterized. To this end, it is proved that, for any $n\geq 1$, every codescent morphism of $n$-quasigroups (resp. $n$-loops) is effective. This statement generalizes our earlier results on qusigroups and loops. Moreover, it is shown that the elements of the amalgamated free products of $n$-quasigroups (resp. $n$-loops) have unique normal forms, and that the varieties of $n$-quasigroups and $n$-loops satisfy the strong amalgamation property. The latter two statements generalize the corresponding old results on quasigroups and loops by Evans.

Effective codescent morphisms of $n$-quasigroups and $n$-loops

Abstract

Effective codescent morphisms of -quasigroups and of -loops are characterized. To this end, it is proved that, for any , every codescent morphism of -quasigroups (resp. -loops) is effective. This statement generalizes our earlier results on qusigroups and loops. Moreover, it is shown that the elements of the amalgamated free products of -quasigroups (resp. -loops) have unique normal forms, and that the varieties of -quasigroups and -loops satisfy the strong amalgamation property. The latter two statements generalize the corresponding old results on quasigroups and loops by Evans.
Paper Structure (3 sections, 20 equations)

This paper contains 3 sections, 20 equations.

Table of Contents

  1. Introduction
  2. The convergent representations of the varieties of n-quasigroups and $n$-loops
  3. Effective codescent morphisms in the varieties of $n$-quasigroups and $n$-loops

Theorems & Definitions (5)

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