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Journal of Logic and Computation Advance Access published online on September 17, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp059
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

On the Structure of Finite Integral Commutative Residuated Chains

Rostislav Horcík

Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou vezí 2, 182 07 Prague 8, Czech Republic; Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 166 27 Prague 6, Czech Republic.
E-mail: horcik{at}cs.cas.cz

Received 8 December 2008.


  Abstract

Among the class of finite integral commutative residuated chains (ICRCs), we identify those algebras which can be obtained as a nuclear retraction of a conuclear contraction of a totally ordered Abelian {ell}-group. We call the ICRCs satisfying this condition regular. Then we discuss the structure of finite regular ICRCs. Finally, we prove that the class of regular members generate a strictly smaller variety than the variety generated by ICRCs.

Keywords: Residuated lattice; ordered residuated monoid; nucleus; conucleus,Abelian lattice-ordered group; free commutative monoid


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