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Cartesian Nets and Groupoids

Published online by Cambridge University Press:  20 November 2018

M. A. Taylor
M. A. Taylor*
Affiliation:
Acadia University, Wolfville, Nova Scotia
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Aczel has conjectured, [1, p. 448], the possibility of developing a net theory for structures more general than quasigroups. Steps in this direction have been taken by Havel who considers nets associated with multigroupoids [2], The work presented here introduces a generalization of 3-nets and their algebraization which is wide enough to encompass most algebraic structures based on a single binary operation.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 3 , September 1973 , pp. 347 - 362
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Aczel, J., Quasigroups, nets and nomograms, Advances in Math. (1) 3 (1965), 383–450.Google Scholar
2. Havel, V. P., Nets associated to multigroupoids, Aequationes Math. 5 (1970), 10–18.Google Scholar
3. Ljapin, E. S., Semigroups, Amer. Math. Soc, Providence, R.I., 1963.Google Scholar
4. Taylor, M. A., Classical, Cartesian and solution nets, Mathematica, 13 (1971), 151–166.Google Scholar