Canonical biassociative groupoids
Journal
Publications de l'Institut Mathématique
Date Issued
2007
Author(s)
Janeva, Biljana
Ilic', Snezhana
Celakoska-Jordanova, Vesna
DOI
102298/PIM0795103J
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.
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.
Subjects
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