Archimedean Residuated Lattices

Abstract

For a residuated lattice A we denote by Ds(A) the lattice of all deductive systems (congruence filters) of A. The aim of this paper is to put in evidence new characterizations for maximal and prime elements of Ds(A) and to characterize archimedean and hyperarchimedean residuated lattices; so we prove some theorems of Nachbin type for residuated lattices. These results generalize to the case of residuated lattices some results earlier obtained by Buşneag and Piciu for the case of BL-algebras.Mathematics Subject Classification 2000: 03G10, 06B20.

States on Hilbert Algebras

“…For another type of states (valuations) defined on Hilbert algebras see [6] (for the case of residuated lattices see [3]). This paper is organized as follows:…”

Untitled

“…P seudo-valuations in residuated lattices was introduced by Busneag [1] where many theorems based on pseudo-valuations in lattice terms and their extension theorem for residuated lattices to pseudo-valuation from valuations are shown using the model of Hilbert algebras [2]. But in fact Pseudo-valuations on a Hilbert algebras was initially introduced by Busneag [3] where it is proved that every pseudo-valuation induces a pseudometric on a Hilbert algebra.…”