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Minimal Varieties of Cancellative Residuated Lattices
by
Rostislav Horcik
Institute of Computer Science, Academy of Sciences of the Czech Republic
The main goal of our talk is to investigate the varieties of cancellative residuated lattices covering the variety V(Z-) generated by the negative cone of integers. We consider the varieties generated by finitely generated submonoids of Z- (note that each such submonoid can be enriched by a residuum so that it forms a cancellative residuated lattice) and show that some of them generate covers of V(Z-). Namely, we prove that each submonoid of Z- generated by two coprime numbers such that the greater one is prime generates a cover of V(Z-). Moreover, we can show that two different pairs of coprime numbers such that the greater one is prime generate different covers of V(Z-). Consequently, it follows that there are infinitely many covers of V(Z-).
Date received: June 16, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxi-44.