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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.