Details
| Original language | English |
|---|---|
| Pages (from-to) | 546-553 |
| Number of pages | 8 |
| Journal | Archiv der Mathematik |
| Volume | 87 |
| Issue number | 6 |
| Publication status | Published - Dec 2006 |
| Externally published | Yes |
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.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Archiv der Mathematik, Vol. 87, No. 6, 12.2006, p. 546-553.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The word problem for involutive residuated lattices and related structures
AU - Wille, Annika M.
N1 - Funding Information: Mathematics Subject Classification (2000): Primary: 06F05, Secondary: 08A50. The author would like to thank the Deutsche Telekom Stiftung for financial support.
PY - 2006/12
Y1 - 2006/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33846815155&partnerID=8YFLogxK
U2 - 10.1007/s00013-006-1795-6
DO - 10.1007/s00013-006-1795-6
M3 - Article
AN - SCOPUS:33846815155
VL - 87
SP - 546
EP - 553
JO - Archiv der Mathematik
JF - Archiv der Mathematik
SN - 0003-889X
IS - 6
ER -