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The word problem for free lattice-ordered groups (and some other free algebras)


Author: Trevor Evans
Journal: Proc. Amer. Math. Soc. 98 (1986), 559-560
MSC: Primary 06F15; Secondary 20F10
DOI: https://doi.org/10.1090/S0002-9939-1986-0861749-2
MathSciNet review: 861749
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Abstract: It is known that in the lattice of all varieties of $ l$-groups, there is a unique maximal proper subvariety. Based on this fact we give a simple algorithm for deciding the word problem in free $ l$-groups. Some other applications are also given.


References [Enhancements On Off] (What's this?)

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  • [2] S. A. Gurchenkov, Varieties of $ l$-groups with the identity $ [{x^p},{y^p}] = 1$ have finite bases, Algebra and Logic 23 (1984), 27-47. MR 781403 (86m:06031)
  • [3] W. C. Holland, The largest proper subvariety of lattice-ordered groups, Proc. Amer. Math. Soc. 57 (1976), 25-28. MR 0406902 (53:10688)
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  • [5] E. B. Scrimger, A large class of small varieties of lattice-ordered groups, Proc. Amer. Math. Soc 51 (1975), 301-306. MR 0384644 (52:5517)

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DOI: https://doi.org/10.1090/S0002-9939-1986-0861749-2
Article copyright: © Copyright 1986 American Mathematical Society

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