Previous |  Up |  Next

# Article

Full entry | PDF   (0.2 MB)
Keywords:
left distributive groupoid; quasitrivial groupoid
Summary:
Left distributive quasitrivial groupoids are completely described and those of them which are subdirectly irreducible are found. There are also determined all left distributive algebras \$A = A(*,\circ)\$ such that \$A(*)\$ is a quasitrivial groupoid.
References:
[DehAd] Dehornoy P.: The adjoint representations of left distributive structures. Comm. Algebra 20 (1992), 1201-1215. MR 1154409
[DehBr] Dehornoy P.: Braid groups and left distributive structures. Transactions AMS, to appear.
[DKM] Drápal A., Kepka T., Musílek M.: Group conjugation has non-trivial LD-identities. Comment. Math. Univ. Carolinae 35 (1994), 219-222. MR 1286567
[JeKe] Ježek J., Kepka T.: Quasitrivial and nearly quasitrivial distributive groupoids and semigroups. Acta Univ. Carol. 19 (1978), 225-237. MR 0509345
[KepQ] Kepka T.: Quasitrivial groupoids and balanced identities. Acta Univ. Carol. 22 49-64. MR 0654381 | Zbl 0516.20033
[LavFr] R. Laver: The left distributive law and the freeness of an algebra of elementary embeddings. Advances in Mathematics 91 (1992), 209-231. MR 1149623 | Zbl 0822.03030

Partner of