Nilpotency and the Hamiltonian property for cancellative residuated lattices

Author:

Colacito Almudena12,Tsinakis Constantine3

Affiliation:

1. Mathematical Institute, University of Bern, 3012 Bern, Switzerland

2. Laboratoire J. A. Dieudonné, Université Cóte d’Azur, 06108 Nice, France

3. Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA

Abstract

This paper studies nilpotent and Hamiltonian cancellative residuated lattices and their relationship with nilpotent and Hamiltonian lattice-ordered groups. In particular, results about lattice-ordered groups are extended to the domain of residuated lattices. The two key ingredients that underlie the considerations of this paper are the categorical equivalence between Ore residuated lattices and lattice-ordered groups endowed with a suitable modal operator; and Malcev’s description of nilpotent groups of a given nilpotency class c in terms of a semigroup equation.

Funder

Swiss National Science Foundation

Marie Skłodowska-Curie

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

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