×

zbMATH — the first resource for mathematics

The semigroup of varieties of weakly associative lattice groups. (English) Zbl 0854.06025
Summary: We prove that the varieties of weakly associative lattice groups form an ordered semigroup with one distributive law.

MSC:
06F15 Ordered groups
06B20 Varieties of lattices
06F05 Ordered semigroups and monoids
08B99 Varieties
PDF BibTeX XML Cite
References:
[1] Glass A. M. W., Holland W. C., McCleary S.: The structure of l-group varieties. Alg. Univ. 10 (1980), 1-20. · Zbl 0439.06013 · doi:10.1007/BF02482885
[2] Fried E.: Tournaments and non-associative lattices. Ann. Univ. Sci. Budapest, Sect. Math. 13 (1970), 151-164. · Zbl 0224.06004
[3] Kurosch A. G.: Lectures on General Algebra. Fizmatgiz, Moscow, 1987
[4] Martinez J.: Varieties of lattice-ordered groups. Math. Z. 137 (1974), 265-284. · Zbl 0274.20034 · doi:10.1007/BF01214370 · eudml:172072
[5] Neumann H.: Varieties of Groups. Springer Verlag, New York, 1967. · Zbl 0251.20001
[6] Rachůnek J.: Semi-ordered groups. Acta Univ. Palacki. Olomuc., Fac. rer. nat. 61 (1979), 5-20.
[7] Rachůnek J.: Solid subgroups of weaky associative lattice groups. Acta Univ. Palacki. Olomuc., Fac. rer. nat. 105, Math. 31 (1992), 13-24. · Zbl 0776.06016
[8] Rachůnek J.: On some varieties of weakly associative lattice groups. Czechoslovak Math. J. · Zbl 0870.06016
[9] Reilly N. R.: Varieties of lattice-ordered groups. Lattice-Ordered Groups (Advances and techniques) (eds. A. M. W. Glass and W.C. Holland), 228-277, Kluwer, Dordrecht-Boston-London, 1989.
[10] Skala H.: Trellis Theory. Memoirs AMS, Providence, 1972. · Zbl 0242.06004
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.