Subject: groupoid, variety, free groupoid

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Year: 2004

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Type: Article

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Title: Free groupoids with x^{2}x^{2}=x^{3}x^{3}

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Author: Celakoska-Jordanova, Vesna

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Abstract: A description of free objects in the variety V of groupoids defined by the identity x^{2}x^{2}=x^{3}x^{3} is obtained. The following method is used: one of the sides of the identity is considered as "suitable" and the other as "unsuitable" one. First, the left-hand side x^{2}x^{2}is chosen as "suitable" and the set of elements of F (F being an absolutely free groupoid with a basis B) containing no parts that have the form x^{3}x^{3} is taken as a "candidate" for the carrier of the desired free object in V. Continuing this procedure, a V-free object is obtained. Another construction of V-free object is obtained by choosing the right-hand side x^{3}x^{3} as "suitable" one.

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Publisher: Faculty of Natural Sciences and Mathematics, Skopje

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Relation: Free algebraic structures, Macedonian Academy of Sciences and Arts

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Identifier: oai:repository.ukim.mk:20.500.12188/2032
Identifier: http://hdl.handle.net/20.500.12188/2032

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