×

zbMATH — the first resource for mathematics

Free distributive groupoids. (English) Zbl 0686.20041
Let F be an absolutely free groupoid and E a free monoid of rank 2. If r,s,u,v,w\(\in F\) are such that \(r=u.vw\) is a subterm of s and if \(e\in E\) is its address in s, then \(\bar e(s)\) is the term obtained from s after replacing r by uv.uw. All these partial transformations \(\bar e,\) \(e\in E\), generate a monoid and the main result of the paper is the following: Theorem. Let \(f,g\in S\). Then \(hf=kg\) for some \(h,k\in S\) such that \(dom(hf)=dom(f)\cap dom(g)\).
Reviewer: T.Kepka

MSC:
20M05 Free semigroups, generators and relations, word problems
08B05 Equational logic, Mal’tsev conditions
20M20 Semigroups of transformations, relations, partitions, etc.
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bourbaki, N., Algébre, I, (1970), Hermann Paris
[2] Bruck, R., A survey of binary systems, (1958), Springer Berlin · Zbl 0081.01704
[3] Dehornoy, P., Infinite products in monoids, Semigroup forum, 34, 21-68, (1986) · Zbl 0601.20061
[4] Dehornoy, P., π11-complete families of elementary embeddings, Ann. pure appl. logic, 3, 257-287, (1988) · Zbl 0646.03030
[5] P. Dehornoy, Algebraic properties of the shift mapping, Proc. Amer. Math. Soc., submitted. · Zbl 0679.20058
[6] Dougherty, R., Notes on critical points of elementary embeddings, Circulated notes, (1988)
[7] Joyce, D., A classifying invariant of knots, the knot quandle, J. pure appl. algebra, 23, 37-66, (1982) · Zbl 0474.57003
[8] Kepka, T., Notes on left distributive groupoids, Acta univ. carolinae math. phys., 22, 23-37, (1981) · Zbl 0517.20048
[9] Knuth, D.E.; Bendix, P.B., Simple word problems in universal algebras, (), 263-297 · Zbl 0188.04902
[10] Moschovakis, Y., Descriptive set theory, (1980), North-Holland Amsterdam · Zbl 0433.03025
[11] Solovay, R.; Reinhardt, W.; Kanamori, A., Strong axioms of infinity and elementary embeddings, Ann. math. logic., 13, 73-116, (1978) · Zbl 0376.02055
[12] Soublin, J-P., Etude algébrique de la notion de moyenne, J. math. pures appl., 50, 253-264, (1971) · Zbl 0186.03301
[13] Stein, S., Left distributive quasigroups, Proc. amer. math. soc., 10, 577-578, (1959) · Zbl 0093.01902
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.