Subdirectly irreducible non-idempotent left symmetric left distributive groupoids

Emil Jeřábek; Tomáš Kepka; David Stanovský

Discussiones Mathematicae - General Algebra and Applications (2005)

  • Volume: 25, Issue: 2, page 235-257
  • ISSN: 1509-9415

Abstract

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We study groupoids satisfying the identities x·xy = y and x·yz = xy·xz. Particularly, we focus our attention at subdirectlyirreducible ones, find a description and charecterize small ones.

How to cite

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Emil Jeřábek, Tomáš Kepka, and David Stanovský. "Subdirectly irreducible non-idempotent left symmetric left distributive groupoids." Discussiones Mathematicae - General Algebra and Applications 25.2 (2005): 235-257. <http://eudml.org/doc/287712>.

@article{EmilJeřábek2005,
abstract = {We study groupoids satisfying the identities x·xy = y and x·yz = xy·xz. Particularly, we focus our attention at subdirectlyirreducible ones, find a description and charecterize small ones.},
author = {Emil Jeřábek, Tomáš Kepka, David Stanovský},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {groupoid; left distributive; left symmetric; subdirectly irreducible; left distributive groupoids; left symmetric groupoids; subdirectly irreducible groupoids},
language = {eng},
number = {2},
pages = {235-257},
title = {Subdirectly irreducible non-idempotent left symmetric left distributive groupoids},
url = {http://eudml.org/doc/287712},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Emil Jeřábek
AU - Tomáš Kepka
AU - David Stanovský
TI - Subdirectly irreducible non-idempotent left symmetric left distributive groupoids
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2005
VL - 25
IS - 2
SP - 235
EP - 257
AB - We study groupoids satisfying the identities x·xy = y and x·yz = xy·xz. Particularly, we focus our attention at subdirectlyirreducible ones, find a description and charecterize small ones.
LA - eng
KW - groupoid; left distributive; left symmetric; subdirectly irreducible; left distributive groupoids; left symmetric groupoids; subdirectly irreducible groupoids
UR - http://eudml.org/doc/287712
ER -

References

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  1. [1] S. Burris and H.P. Sankappanavar, A course in universal algebra, GTM 78, Springer 1981. Zbl0478.08001
  2. [2] P. Dehornoy, Braids and self-distributivity, Progress in Math. 192, Birkhäuser Basel 2000. Zbl0958.20033
  3. [3] D. Joyce, Simple quandles, J. Algebra 79 (1982), 307-318. Zbl0514.20018
  4. [4] T. Kepka, Non-idempotent left symmetric left distributive groupoids, Comment. Math. Univ. Carolinae 35 (1994), 181-186. Zbl0807.20057
  5. [5] T. Kepka and P. Nemec, Selfdistributive groupoids. A1. Non-indempotent left distributive groupoids, Acta Univ. Carolin. Math. Phys. 44/1 (2003), 3-94. Zbl1080.20060
  6. [6] H. Nagao, A remark on simple symmetric sets, Osaka J. Math. 16 (1979), 349-352. Zbl0417.20028
  7. [7] B. Roszkowska-Lech, Subdirectly irreducible symmetric idempotent entropic groupoids, Demonstratio Math. 32/3 (1999), 469-484. Zbl0951.20050
  8. [8] D. Stanovský, A survey of left symmetric left distributive groupoids, available at http://www.karlin.mff.cuni.cz/~stanovsk/math/survey.pdf. 
  9. [9] D. Stanovský, Left symmetric left distributive operations on a group, Algebra Universalis 54/1 (2003), 97-103. Zbl1085.20043
  10. [10] M. Takasaki, Abstractions of symmetric functions, Tôhoku Math. Journal 49 (1943), 143-207 (Japanese). 

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