The word problem for involutive residuated lattices and related structures

authored by: Annika M. Wille
Abstract: It will be shown that the word problem is undecidable for involutive residuated lattices, for finite involutive residuated lattices and certain related structures like residuated lattices. The proof relies on the fact that the monoid reduct of a group can be embedded as a monoid into a distributive involutive residuated lattice. Thus, results about groups by P. S. Novikov and W. W. Boone and about finite groups by A. M. Slobodskoi can be used. Furthermore, for any non-trivial lattice variety V, the word problem is undecidable for those involutive residuated lattices and finite involutive residuated lattices whose lattice reducts belong to V. In particular, the word problem is undecidable for modular and distributive involutive residuated lattices.
External Organisation(s): Technische Universität Darmstadt
Type: Article
Journal: Archiv der Mathematik
Volume: 87
Pages: 546-553
No. of pages: 8
ISSN: 0003-889X
Publication date: 12.2006
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: General Mathematics
Electronic version(s): https://doi.org/10.1007/s00013-006-1795-6 (Access: Unknown)
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