Free groupoids with x^{2}x^{2}=x^{3}x^{3}
Journal
Mathematica Macedonica
Date Issued
2004
Author(s)
Celakoska-Jordanova, Vesna
Abstract
A description of free objects in the variety V of groupoids defined by the identity x^{2}x^{2}=x^{3}x^{3} is obtained. The following method is used: one of the sides of the identity is considered as "suitable" and the other as "unsuitable" one. First, the left-hand side x^{2}x^{2}is chosen as "suitable" and the set of elements of F (F being an absolutely free groupoid with a basis B) containing no parts that have the form x^{3}x^{3} is taken as a "candidate" for the carrier of the desired free object in V. Continuing this procedure, a V-free object is obtained. Another construction of V-free object is obtained by choosing the right-hand side x^{3}x^{3} as "suitable" one.
Subjects
File(s)![Thumbnail Image]()
Loading...
Name
Free groupoids with x2x2=x3x3.pdf
Size
850.24 KB
Format
Adobe PDF
Checksum
(MD5):8b8f1fbbc62f95216e1d9784835a0ef9