A closure condition which is equivalent to the Thomsen condition in quasigroups.
Stochastica (1983)
- Volume: 7, Issue: 1, page 11-16
- ISSN: 0210-7821
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topTaylor, M. A.. "A closure condition which is equivalent to the Thomsen condition in quasigroups.." Stochastica 7.1 (1983): 11-16. <http://eudml.org/doc/38875>.
@article{Taylor1983,
abstract = {In this note it is shown that the closure condition, X1Y2 = X2Y1, X1Y4 = X2Y3, X3Y3 = X4Y1 --> X4Y2 = X3Y4, (and its dual) is equivalent to the Thomsen condition in quasigroups but not in general. Conditions are also given under which groupoids satisfying it are principal homotopes of cancellative, abelian semigroups, or abelian groups.},
author = {Taylor, M. A.},
journal = {Stochastica},
keywords = {Grupoides; Teoría de grupos; Thomsen condition; quasigroups; groupoids; principal homotopes},
language = {eng},
number = {1},
pages = {11-16},
title = {A closure condition which is equivalent to the Thomsen condition in quasigroups.},
url = {http://eudml.org/doc/38875},
volume = {7},
year = {1983},
}
TY - JOUR
AU - Taylor, M. A.
TI - A closure condition which is equivalent to the Thomsen condition in quasigroups.
JO - Stochastica
PY - 1983
VL - 7
IS - 1
SP - 11
EP - 16
AB - In this note it is shown that the closure condition, X1Y2 = X2Y1, X1Y4 = X2Y3, X3Y3 = X4Y1 --> X4Y2 = X3Y4, (and its dual) is equivalent to the Thomsen condition in quasigroups but not in general. Conditions are also given under which groupoids satisfying it are principal homotopes of cancellative, abelian semigroups, or abelian groups.
LA - eng
KW - Grupoides; Teoría de grupos; Thomsen condition; quasigroups; groupoids; principal homotopes
UR - http://eudml.org/doc/38875
ER -
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