Subject: Groupoid, subgroupoid generated by two elements, subsemigroup, free groupoid, canonical groupoid.
Year: 2007
Type: Article
Title: Canonical biassociative groupoids
Author: Janeva, Biljana
Author: Ilic', Snezhana
Author: Celakoska-Jordanova, Vesna
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.
Publisher: Mathematical Institute of the Serbian Academy of Sciences and Arts
Relation: Publications de l'Institut Mathématique
Identifier: oai:repository.ukim.mk:20.500.12188/2029
Identifier: http://hdl.handle.net/20.500.12188/2029Identifier: 102298/PIM0795103J
