Goracinova Ilieva, Lidija (2003) Конструкција на слободните групоиди со верига парцијалните групоиди: слободен Штaјнов групоид. Годишен зборник - Annual Miscellaneous Collection.
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КОНСТРУКЦИЈА НА СЛОБОДНИ ГРУПОИДИ.pdf Download (393kB) | Preview |
Abstract
Every nontrivial variety of groupoids is generated by its free groupoid which can be obtained as a quotient-groupoid of the absolutely free groupoid over a countable set. The problem of the construction of a free groupoid in a variety is equivalent to the problem of discovering an efficient description of the congruence which is an object of the factorization, or to the problem of finding the set of identities of the free groupoid which equals to the set of common identities of all groupoids in the variety. In many cases, this is not an easy assignment, and there is no general method which can be applied to each particular variety.
Here a new approach for constructing free objects is proposed, by using a chain of partial groupoids which satisfy the identities of the variety. Every partial groupoid of the chain represents a better approximation than the previous one. The wanted free groupoid is built gradually as a union of the partial groupoids.
The description of the procedure is illustrated by the construction of a free groupoid in the variety defined by Stein identity (xy)y≈yx.
| Item Type: | Article |
|---|---|
| Subjects: | Social Sciences > Educational sciences |
| Divisions: | Faculty of Educational Science |
| Depositing User: | Sanja Stefanova |
| Date Deposited: | 24 Dec 2012 12:07 |
| Last Modified: | 24 Dec 2012 12:07 |
| URI: | https://eprints.ugd.edu.mk/id/eprint/4318 |
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