Equations in the theory of Q-distributive lattices

A Q-distributive lattice is an algebra (L, ∨, ∧, ∇, 0, 1) of type (2, 2, 1, 0, 0) such that (L, ∨, ∧, 0, 1) is a bounded distributive lattice and ∇ satisfies the equations ∇0 = 0, x ∧ ∇x = x, ∇(x ∨ y) = ∇x ∨ ∇y and ∇(x ∧ ∇y) = ∇x ∧ ∇y. The aim of this paper is to find, for each proper subvariety of...

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Detalles Bibliográficos
Autor principal: Petrovich, Alejandro Gustavo
Publicado: 1997
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0012365X_v175_n1-3_p211_Petrovich
http://hdl.handle.net/20.500.12110/paper_0012365X_v175_n1-3_p211_Petrovich
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_0012365X_v175_n1-3_p211_Petrovich2023-06-08T14:35:21Z Equations in the theory of Q-distributive lattices Petrovich, Alejandro Gustavo A Q-distributive lattice is an algebra (L, ∨, ∧, ∇, 0, 1) of type (2, 2, 1, 0, 0) such that (L, ∨, ∧, 0, 1) is a bounded distributive lattice and ∇ satisfies the equations ∇0 = 0, x ∧ ∇x = x, ∇(x ∨ y) = ∇x ∨ ∇y and ∇(x ∧ ∇y) = ∇x ∧ ∇y. The aim of this paper is to find, for each proper subvariety of the variety of Q-distributive lattices, an equation which determines it, relatively to the whole variety, as well as to give a characterization of the minimum number of variables needed in such equation. Fil:Petrovich, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1997 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0012365X_v175_n1-3_p211_Petrovich http://hdl.handle.net/20.500.12110/paper_0012365X_v175_n1-3_p211_Petrovich
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description A Q-distributive lattice is an algebra (L, ∨, ∧, ∇, 0, 1) of type (2, 2, 1, 0, 0) such that (L, ∨, ∧, 0, 1) is a bounded distributive lattice and ∇ satisfies the equations ∇0 = 0, x ∧ ∇x = x, ∇(x ∨ y) = ∇x ∨ ∇y and ∇(x ∧ ∇y) = ∇x ∧ ∇y. The aim of this paper is to find, for each proper subvariety of the variety of Q-distributive lattices, an equation which determines it, relatively to the whole variety, as well as to give a characterization of the minimum number of variables needed in such equation.
author Petrovich, Alejandro Gustavo
spellingShingle Petrovich, Alejandro Gustavo
Equations in the theory of Q-distributive lattices
author_facet Petrovich, Alejandro Gustavo
author_sort Petrovich, Alejandro Gustavo
title Equations in the theory of Q-distributive lattices
title_short Equations in the theory of Q-distributive lattices
title_full Equations in the theory of Q-distributive lattices
title_fullStr Equations in the theory of Q-distributive lattices
title_full_unstemmed Equations in the theory of Q-distributive lattices
title_sort equations in the theory of q-distributive lattices
publishDate 1997
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0012365X_v175_n1-3_p211_Petrovich
http://hdl.handle.net/20.500.12110/paper_0012365X_v175_n1-3_p211_Petrovich
work_keys_str_mv AT petrovichalejandrogustavo equationsinthetheoryofqdistributivelattices
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