El reticulado de subvariedades de MG
Contenido: - T-normas. - Hoops y BL-algebras. - Subvariedad MG. - Λ(MG). - Bases ecuacionales. - Álgebras libres. - Bibliografía.
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| Formato: | Objeto de conferencia |
| Lenguaje: | Español |
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2019
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/164538 |
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I19-R120-10915-164538 |
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I19-R120-10915-1645382024-04-08T20:47:33Z http://sedici.unlp.edu.ar/handle/10915/164538 El reticulado de subvariedades de MG The lattice of subvarieties of the variety MG Díaz Varela, Patricio Lubomirsky, Noemí 2019-06 2019 2024-04-08T13:39:36Z es Ciencias Exactas Matemática Álgebra Contenido: - T-normas. - Hoops y BL-algebras. - Subvariedad MG. - Λ(MG). - Bases ecuacionales. - Álgebras libres. - Bibliografía. BL-algebras were introduced by Hájek (see [5]) to formalize fuzzy logics in which the conjunction is interpreted by continuous t-norms over the real interval [0;1]. These algebras form a variety, usually called BL. In this work we will concentrate in the subvariety MG ⊆ BL generated by the ordinal sum of the algebra [0;1]MV and the Gödel hoop [0;1]G, that is, generated by A = [0;1]MV ⊕ [0;1]G. Though it is well-known that [0;1]G is decomposable as an infinite ordinal sum of two-elements Boolean algebra, the idea is to treat it as a whole block. The elements of this block are the dense elements of the generating chain and the elements in [0;1]MV are usually called regular elements of A: The main advantage of this approach, is that unlike the work done in [3] and [1], when the number n of generators of the free algebra increase the generating chain remains fixed. This provides a clear insight of the role of the two main blocks of the generating chain in the description of the functions in the free algebra: the role of the regular elements and the role of the dense elements. We have a functional representation for the free algebra FreeMG (n). To define this functions we need to decompose the domain Aⁿ = ([0;1]MV ⊕ [0;1]G)ⁿ in a finite number of pieces. In each piece a function F ∈ FreeMG (n) coincides either with McNaughton functions or functions of FreeG (n). Using [2] and [4] we give a description of the elements in the lattice of subvarieties of the variety MG and the equational characterization of them. Facultad de Ciencias Exactas Departamento de Matemática Objeto de conferencia Objeto de conferencia http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) application/pdf |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Español |
| topic |
Ciencias Exactas Matemática Álgebra |
| spellingShingle |
Ciencias Exactas Matemática Álgebra Díaz Varela, Patricio Lubomirsky, Noemí El reticulado de subvariedades de MG |
| topic_facet |
Ciencias Exactas Matemática Álgebra |
| description |
Contenido:
- T-normas.
- Hoops y BL-algebras.
- Subvariedad MG.
- Λ(MG).
- Bases ecuacionales.
- Álgebras libres.
- Bibliografía. |
| format |
Objeto de conferencia Objeto de conferencia |
| author |
Díaz Varela, Patricio Lubomirsky, Noemí |
| author_facet |
Díaz Varela, Patricio Lubomirsky, Noemí |
| author_sort |
Díaz Varela, Patricio |
| title |
El reticulado de subvariedades de MG |
| title_short |
El reticulado de subvariedades de MG |
| title_full |
El reticulado de subvariedades de MG |
| title_fullStr |
El reticulado de subvariedades de MG |
| title_full_unstemmed |
El reticulado de subvariedades de MG |
| title_sort |
el reticulado de subvariedades de mg |
| publishDate |
2019 |
| url |
http://sedici.unlp.edu.ar/handle/10915/164538 |
| work_keys_str_mv |
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1807222883242475520 |