Subject: groupoid, free groupoid, injective groupoid

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Year: 2007

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Type: Article

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Title: Free objects in the variety of groupoids defined by the identity xx^(m)=x(m+1)

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Author: Celakoska-Jordanova, Vesna

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Abstract: A construction of free objects in the variety V_(m) of groupoids defined by the identity xx^(m)=x^(m+1), where m is a fixed positive integer, and (k) is a transformation of a groupoid G=(G, .), defined by x^(0)=x, x^(k+1)=(x^(k))^2, is given. A class of injective groupoids in V_(m) is defined and a corresponding Bruck theorem for this variety is proved. It is shown that the class of free groupoids in V_(m) is a proper subclass of the class of injective groupoids in V_(m) .

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Publisher: Faculty of Mathematics and Natural Sciences, South-West University "Neofit Rilsky", Blagoevgrad, Bulgaria

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Relation: Proc. of the Second Int. Sc. Conf. 6-10.06.2007, FMNS, South-West University "Neofit Rilsky", Blagoevgrad

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Identifier: oai:repository.ukim.mk:20.500.12188/1967
Identifier: http://hdl.handle.net/20.500.12188/1967

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