Geodesic
Canonical Biassociative Groupoids
Publications de l'Institut Mathématique, _N_S_81 (2007) no. 95, p. 103

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In the paper \emph{Free biassociative groupoids}, the variety of biassociative groupoids (i.e., groupoids that satisfy the condition: every subgroupoid generated by at most two elements is a subsemigroup) is considered and free objects are constructed using a chain of partial biassociative groupoids that satisfy certain properties. The obtained free objects in this variety are not canonical. By a \textit{canonical groupoid} in a variety $\mathcal{V}$ of groupoids we mean a free groupoid $(R,*)$ in $\mathcal{V}$ with a free basis $B$ such that the carrier $R$ is a subset of the absolutely free groupoid $(T_B,\cdot)$ with the free basis $B$ and $(tu\in R\;\Rightarrow\;t,u\in R\,\,\\,\,t*u=tu)$. In the present paper, a canonical description of free objects in the variety of biassociative groupoids is obtained.
DOI : 10.2298/PIM0795103J
Classification : 08B20 03C05
Keywords: Groupoid, subgroupoid generated by two elements, subsemigroup, free groupoid, canonical groupoid 
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     title = {Canonical {Biassociative} {Groupoids}},
     journal = {Publications de l'Institut Math\'ematique},
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Biljana Janeva; Snežana Ilić; Vesna Celakoska-Jordanova. Canonical Biassociative Groupoids. Publications de l'Institut Mathématique, _N_S_81 (2007) no. 95, p. 103 . doi: 10.2298/PIM0795103J

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