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 -groups, there is a unique maximal proper subvariety. Based on this fact we give a simple algorithm for deciding the word problem in free -groups. Some other applications are also given.

**[1]**T. Evans, K. Mandelberg and M. F. Neff,*Embedding algebras with solvable word problem in simple algebras-some Boone-Higman type theorems*, Logic Colloquium '73, Studies in Logic, vol. 80, North-Holland, Amsterdam, 1975, pp. 259-277. MR**0389568 (52:10399)****[2]**S. A. Gurchenkov,*Varieties of**-groups with the identity**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)****[4]**W. C. Holland and S. H. McCleary,*Solvability of the word problem in free lattice-ordered groups*, Houston J. Math**5**(1979), 99-105. MR**533643 (80f:06018)****[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