In this paper we shall introduce the notion of σ- ideals in the variety of pseudocomplemented residuated lattices.We shall also give some characterizations of the stonean pseudocomplemented residuated lattices.

Given an integral commutative residuated lattice L, the product L × L can be endowed with the structure of a commutative residuated lattice with involution that we call a twist-product. In the present paper, we study the ...

In this paper we deal with varieties of commutative residuated lattices that arise from a specific kind of construction: the twist-product of a lattice. Twist-products were first considered by Kalman in 1958 to deal with ...

In this paper we prove that the free pseudocomplemented residuated lattices are decomposable if and only if they are Stone, i.e., if and only if they satisfy the identity ¬x ∨ ¬¬x = 1. Some applications are given.

In this article we study in detail the regular elements of a bounded, commutative and integral residuated lattice. We introduce the notion of a regular variety and explore its relationship with the Kolmogorov negative ...

We follow the ideas given by Chen and Grätzer to represent Stone algebras and adapt them for the case of Stonean residuated lattices. Given a Stonean residuated lattice, we consider the triple formed by its Boolean skeleton, ...