Difference between revisions of "Free groupoid"
From Encyclopedia of Mathematics
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| − | A free algebra in the variety of groupoids. The free groupoid on a set | + | {{TEX|done}} |
| + | A free algebra in the variety of groupoids. The free groupoid on a set $X$ of free generators coincides with the set of all bracketed words (cf. [[Word|Word]]) in the elements of $X$ (each symbol is assumed to be taken in brackets, and the brackets are arranged so that each time only two brackets are multiplied out). The product of the words (a) and (b) is the word ((a)(b)). | ||
Revision as of 21:23, 19 June 2014
A free algebra in the variety of groupoids. The free groupoid on a set $X$ of free generators coincides with the set of all bracketed words (cf. Word) in the elements of $X$ (each symbol is assumed to be taken in brackets, and the brackets are arranged so that each time only two brackets are multiplied out). The product of the words (a) and (b) is the word ((a)(b)).
How to Cite This Entry:
Free groupoid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Free_groupoid&oldid=16388
Free groupoid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Free_groupoid&oldid=16388
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article