BECAS
NAGY Agustin Leonel
artículos
Título:
Dualities for subresiduated lattices
Autor/es:
CELANI, SERGIO; SAN MARTÍN, HERNÁN; NAGY, AGUSTÍN
Revista:
ALGEBRA UNIVERSALIS
Editorial:
BIRKHAUSER VERLAG AG
Referencias:
Lugar: BASEL; Año: 2021
ISSN:
0002-5240
Resumen:
A subresiduated lattice is a pair $(A,D)$, where $A$ is a boundeddistributive lattice, $D$ is a bounded sublattice of $A$ and forevery $a,bin A$ there is $cin D$ such that for all $din D$,$dwe aleq b$ if and only if $dleq c$. This $c$ is denoted by$aa b$. This pair can be regarded as an algebra$left$ of type $(2,2,2,0,0)$ where $D={ain A:1a a=a}$.The class of subresiduated lattices is a variety which properlycontains to the variety of Heyting algebras.In this paper we present dual equivalences for the algebraic categoryof subresiduated lattices. More precisely, we develop a spectral styleduality and a bitopological style duality for this algebraic category.Finally we study the connections of these results with a known Priestleystyle duality for the algebraic category of subresiduated lattices.
