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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todo:paper_0012365X_v175_n1-3_p211_Petrovich2023-10-03T14:10:19Z Equations in the theory of Q-distributive lattices Petrovich, A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0012365X_v175_n1-3_p211_Petrovich |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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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. |
| format |
JOUR |
| author |
Petrovich, A. |
| spellingShingle |
Petrovich, A. Equations in the theory of Q-distributive lattices |
| author_facet |
Petrovich, A. |
| author_sort |
Petrovich, A. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_0012365X_v175_n1-3_p211_Petrovich |
| work_keys_str_mv |
AT petrovicha equationsinthetheoryofqdistributivelattices |
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1807318588449619968 |