Cancellative Residuated Lattices Arising on 2-Generated Submonoids of Natural Numbers

Authors: Rostislav Horčík
Publication year: 2010
Publication type: Článek v odborném periodiku
Periodical: Algebra Universalis
Projects: Complexity of t-norm based logics - algebraic and proof-theoretical approach
Bibliographic citation: HORČÍK, Rostislav. Cancellative Residuated Lattices Arising on 2-Generated Submonoids of Natural Numbers. Algebra Universalis. 2010, 63(2-3), 261-274. ISSN 0002-5240. E-ISSN 1420-8911
Dostupné z: doi:10.1007/s00012-010-0076-1
DOI: 10.1007/s00012-010-0076-1
ID: 348399

Abstract

It is known that there are only two cancellative atoms in the subvariety lattice of residuated lattices, namely the variety of Abelian l-groups generated by the additive l-group of integers and the variety V generated by the negative cone of this l-group. In this paper we consider all cancellative residuated chains arising on 2-generated submonoids of natural numbers and show that almost all of them generate a cover of V. This proves that there are infinitely many covers above V which are commutative, integral, and representable.