ArticleOriginal scientific text
Title
Subdirectly irreducible non-idempotent left symmetric left distributive groupoids
Authors 1, 2, 2
Affiliations
- Mathematical Institute, Academy of Sciences, Prague, Czech Republic
- Charles University in Prague, Czech Republic
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.
Keywords
groupoid, left distributive, left symmetric, subdirectly irreducible
Bibliography
- S. Burris and H.P. Sankappanavar, A course in universal algebra, GTM 78, Springer 1981.
- P. Dehornoy, Braids and self-distributivity, Progress in Math. 192, Birkhäuser Basel 2000.
- D. Joyce, Simple quandles, J. Algebra 79 (1982), 307-318.
- T. Kepka, Non-idempotent left symmetric left distributive groupoids, Comment. Math. Univ. Carolinae 35 (1994), 181-186.
- T. Kepka and P. Nemec, Selfdistributive groupoids. A1. Non-indempotent left distributive groupoids, Acta Univ. Carolin. Math. Phys. 44/1 (2003), 3-94.
- H. Nagao, A remark on simple symmetric sets, Osaka J. Math. 16 (1979), 349-352.
- B. Roszkowska-Lech, Subdirectly irreducible symmetric idempotent entropic groupoids, Demonstratio Math. 32/3 (1999), 469-484.
- D. Stanovský, A survey of left symmetric left distributive groupoids, available at http://www.karlin.mff.cuni.cz/~stanovsk/math/survey.pdf.
- D. Stanovský, Left symmetric left distributive operations on a group, Algebra Universalis 54/1 (2003), 97-103.
- M. Takasaki, Abstractions of symmetric functions, Tôhoku Math. Journal 49 (1943), 143-207 (Japanese).