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http://hdl.handle.net/20.500.12188/2029
Наслов: | Canonical biassociative groupoids | Authors: | Janeva, Biljana Ilic', Snezhana Celakoska-Jordanova, Vesna |
Keywords: | Groupoid, subgroupoid generated by two elements, subsemigroup, free groupoid, canonical groupoid. | Issue Date: | 2007 | Publisher: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Journal: | Publications de l'Institut Mathématique | Abstract: | In the paper "Free biassociative groupoids", the variety of biassociative groupoids (i.e., groupoids satisfying 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 canonical groupoid in a variety V of groupoids we mean a free groupoid (R, ∗) in V with a free basis B such that the carrier R is a subset of the absolutely free groupoid (T_B, ·) with the free basis B and (tu ∈ R ⇒ t, u ∈ R & t∗u = tu). In the present paper, a canonical description of free objects in the variety of biassociative groupoids is obtained. | URI: | http://hdl.handle.net/20.500.12188/2029 | DOI: | 102298/PIM0795103J |
Appears in Collections: | Faculty of Natural Sciences and Mathematics: Journal Articles |
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