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EVANS' NORMAL FORM THEOREM REVISITED.
- Source :
-
International Journal of Algebra & Computation . Dec2007, Vol. 17 Issue 8, p1577-1592. 16p. 1 Diagram. - Publication Year :
- 2007
-
Abstract
- Evans defined quasigroups equationally, and proved a Normal Form Theorem solving the word problem for free extensions of partial Latin squares. In this paper, quasigroups are redefined as algebras with six basic operations related by triality, manifested as coupled right and left regular actions of the symmetric group on three symbols. Triality leads to considerable simplifications in the proof of Evans' Normal Form Theorem, and makes it directly applicable to each of the six major varieties of quasigroups defined by subgroups of the symmetric group. Normal form theorems for the corresponding varieties of idempotent quasigroups are obtained as immediate corollaries. [ABSTRACT FROM AUTHOR]
- Subjects :
- *QUASIGROUPS
*GROUP theory
*DIVISION algebras
*ALGEBRA
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 02181967
- Volume :
- 17
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- International Journal of Algebra & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 27943275
- Full Text :
- https://doi.org/10.1142/S0218196707004323