Slim groupoids
Czechoslovak Mathematical Journal (2007)
- Volume: 57, Issue: 4, page 1275-1288
- ISSN: 0011-4642
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topJežek, Jaroslav. "Slim groupoids." Czechoslovak Mathematical Journal 57.4 (2007): 1275-1288. <http://eudml.org/doc/31192>.
@article{Ježek2007,
abstract = {Slim groupoids are groupoids satisfying $x(yz)x̄z$. We find all simple slim groupoids and all minimal varieties of slim groupoids. Every slim groupoid can be embedded into a subdirectly irreducible slim groupoid. The variety of slim groupoids has the finite embeddability property, so that the word problem is solvable. We introduce the notion of a strongly nonfinitely based slim groupoid (such groupoids are inherently nonfinitely based) and find all strongly nonfinitely based slim groupoids with at most four elements; up to isomorphism, there are just two such groupoids.},
author = {Ježek, Jaroslav},
journal = {Czechoslovak Mathematical Journal},
keywords = {groupoid; variety; nonfinitely based; simple slim groupoids; minimal varieties of slim groupoids; subdirectly irreducible slim groupoids; word problem; nonfinitely based slim groupoids},
language = {eng},
number = {4},
pages = {1275-1288},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Slim groupoids},
url = {http://eudml.org/doc/31192},
volume = {57},
year = {2007},
}
TY - JOUR
AU - Ježek, Jaroslav
TI - Slim groupoids
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 4
SP - 1275
EP - 1288
AB - Slim groupoids are groupoids satisfying $x(yz)x̄z$. We find all simple slim groupoids and all minimal varieties of slim groupoids. Every slim groupoid can be embedded into a subdirectly irreducible slim groupoid. The variety of slim groupoids has the finite embeddability property, so that the word problem is solvable. We introduce the notion of a strongly nonfinitely based slim groupoid (such groupoids are inherently nonfinitely based) and find all strongly nonfinitely based slim groupoids with at most four elements; up to isomorphism, there are just two such groupoids.
LA - eng
KW - groupoid; variety; nonfinitely based; simple slim groupoids; minimal varieties of slim groupoids; subdirectly irreducible slim groupoids; word problem; nonfinitely based slim groupoids
UR - http://eudml.org/doc/31192
ER -
References
top- Embeddability and the word problem, J. London Math. Soc. 28 (1953), 76–80. (1953) Zbl0050.02801MR0053915
- 10.1142/S0218196796000040, Int. J. Algebra and Computation 6 (1996), 49–104. (1996) Zbl0844.08011MR1371734DOI10.1142/S0218196796000040
- Algebras, Lattices, Varieties, Volume I, Wadsworth & Brooks/Cole, Monterey, CA, 1987. (1987) MR0883644
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