Noemí Lubomirsky | Searcharxiv

arXiv2026

Hemi-Nelson algebras

The aim of this paper is to generalize the link between Heyting algebras and Nelson algebras, established independently by Fidel and Vakarelov at the end of the 1970s, in the framework of bounded distributive hemi-implicative lattices. For this purpose, we introduce the variety of hemi-Nelson algebras. Moreover, we characterize the lattice of congruences of a hemi-Nelson algebra in terms of certain implicative filters. We also esta\-blish an equivalence between the algebraic category of bounded distributive hemi-implicative lattices and the one of centered hemi-Nelson algebras.

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arXiv2024

Subresiduated Nelson Algebras

In this paper we generalize the well known relation between Heyting algebras and Nelson algebras in the framework of subresiduated lattices. In order to make it possible, we introduce the variety of subresiduated Nelson algebras. The main tool for its study is the construction provided by Vakarelov. Using it, we characterize the lattice of congruences of a subresiduated Nelson algebra through some of its implicative filters. We use this characterization to describe simple and subdirectly irreducible algebras, as well as principal congruences. Moreover, we prove that the variety of subresiduated Nelson algebras has equationally definable principal congruences and also the congruence extension property. Additionally, we present an equational base for the variety generated by the totally ordered subresiduated Nelson algebras. Finally, we show that there exists an equivalence between the algebraic category of subresiduated lattices and the algebraic category of centedred subresiduated Nelson algebras.

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