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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1101, author = {Emil Je\v r\'abek and Tom\'a\v s Kepka and David Stanovsk\'y}, title = {Subdirectly irreducible non-idempotent left symmetric left distributive groupoids}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {25}, year = {2005}, pages = {235-257}, zbl = {1102.20045}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1101} }
Emil Jeřábek; Tomáš Kepka; David Stanovský. Subdirectly irreducible non-idempotent left symmetric left distributive groupoids. Discussiones Mathematicae - General Algebra and Applications, Tome 25 (2005) pp. 235-257. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1101/
[000] [1] S. Burris and H.P. Sankappanavar, A course in universal algebra, GTM 78, Springer 1981. | Zbl 0478.08001
[001] [2] P. Dehornoy, Braids and self-distributivity, Progress in Math. 192, Birkhäuser Basel 2000. | Zbl 0958.20033
[002] [3] D. Joyce, Simple quandles, J. Algebra 79 (1982), 307-318. | Zbl 0514.20018
[003] [4] T. Kepka, Non-idempotent left symmetric left distributive groupoids, Comment. Math. Univ. Carolinae 35 (1994), 181-186. | Zbl 0807.20057
[004] [5] T. Kepka and P. Nemec, Selfdistributive groupoids. A1. Non-indempotent left distributive groupoids, Acta Univ. Carolin. Math. Phys. 44/1 (2003), 3-94. | Zbl 1080.20060
[005] [6] H. Nagao, A remark on simple symmetric sets, Osaka J. Math. 16 (1979), 349-352. | Zbl 0417.20028
[006] [7] B. Roszkowska-Lech, Subdirectly irreducible symmetric idempotent entropic groupoids, Demonstratio Math. 32/3 (1999), 469-484. | Zbl 0951.20050
[007] [8] D. Stanovský, A survey of left symmetric left distributive groupoids, available at http://www.karlin.mff.cuni.cz/~stanovsk/math/survey.pdf.
[008] [9] D. Stanovský, Left symmetric left distributive operations on a group, Algebra Universalis 54/1 (2003), 97-103. | Zbl 1085.20043
[009] [10] M. Takasaki, Abstractions of symmetric functions, Tôhoku Math. Journal 49 (1943), 143-207 (Japanese).