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http://hdl.handle.net/20.500.12188/1967
Title: | Free objects in the variety of groupoids defined by the identity xx^(m)=x(m+1) | Authors: | Celakoska-Jordanova, Vesna | Keywords: | groupoid, free groupoid, injective groupoid | Issue Date: | 2007 | Publisher: | Faculty of Mathematics and Natural Sciences, South-West University "Neofit Rilsky", Blagoevgrad, Bulgaria | Journal: | Proc. of the Second Int. Sc. Conf. 6-10.06.2007, FMNS, South-West University "Neofit Rilsky", Blagoevgrad | Conference: | Second International Scientific Conference, 6-10.06.2007, FMNS, South-West University "Neofit Rilsky", Blagoevgrad, Bulgaria | 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) . | URI: | http://hdl.handle.net/20.500.12188/1967 |
Appears in Collections: | Faculty of Natural Sciences and Mathematics: Conference papers |
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