Affiliation:
1. Faculty of Natural Sciences and Mathematics Ss . Cyril and Methodius University Arhimedova , 3 1000 Skopje Republic of Macedonia ,
Abstract
Abstract
A power-associative n-ary groupoid is an n-ary groupoid
G
such that for every element a ∈ G, the n-ary subgroupoid of
G
generated by a is an n-ary subsemigroup of
G
. The class 𝓟
a
of power-associative n-ary groupoids is a variety. A description of free objects in this variety and their characterization by means of injective n-ary groupoids in 𝓟
a
are obtained.
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