Epimorphisms between finite MV-algebras
Aldo V. Figallo; Marina B. Lattanzi
Mathematica Bohemica (2017)
- Volume: 142, Issue: 4, page 345-355
- ISSN: 0862-7959
Access Full Article
top
Abstract
topHow to cite
topFigallo, Aldo V., and Lattanzi, Marina B.. "Epimorphisms between finite MV-algebras." Mathematica Bohemica 142.4 (2017): 345-355. <http://eudml.org/doc/294300>.
@article{Figallo2017,
abstract = {MV-algebras were introduced by Chang to prove the completeness of the infinite-valued Łukasiewicz propositional calculus. Recently, algebraic theory of MV-algebras has been intensively studied. Wajsberg algebras are just a reformulation of Chang MV-algebras where implication is used instead of disjunction. Using these equivalence, in this paper we provide conditions for the existence of an epimorphism between two finite MV-algebras $A$ and $B$. Specifically, we define the mv-functions with domain in the ordered set of prime elements of $B$ and with range in the ordered set of prime elements of $A$, and prove that every epimorphism from $A$ to $B$ can be uniquely constructed from an mv-function.},
author = {Figallo, Aldo V., Lattanzi, Marina B.},
journal = {Mathematica Bohemica},
keywords = {MV-algebras; mv-function; epimorphism},
language = {eng},
number = {4},
pages = {345-355},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Epimorphisms between finite MV-algebras},
url = {http://eudml.org/doc/294300},
volume = {142},
year = {2017},
}
TY - JOUR
AU - Figallo, Aldo V.
AU - Lattanzi, Marina B.
TI - Epimorphisms between finite MV-algebras
JO - Mathematica Bohemica
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 142
IS - 4
SP - 345
EP - 355
AB - MV-algebras were introduced by Chang to prove the completeness of the infinite-valued Łukasiewicz propositional calculus. Recently, algebraic theory of MV-algebras has been intensively studied. Wajsberg algebras are just a reformulation of Chang MV-algebras where implication is used instead of disjunction. Using these equivalence, in this paper we provide conditions for the existence of an epimorphism between two finite MV-algebras $A$ and $B$. Specifically, we define the mv-functions with domain in the ordered set of prime elements of $B$ and with range in the ordered set of prime elements of $A$, and prove that every epimorphism from $A$ to $B$ can be uniquely constructed from an mv-function.
LA - eng
KW - MV-algebras; mv-function; epimorphism
UR - http://eudml.org/doc/294300
ER -
References
top- Abad, M., Figallo, A., On Łukasiewicz Homomorphisms, Facultad de Filosofía, Humanidades y Artes, Universidad Nacional de San Juan (1992). (1992)
- Berman, J., Blok, W. J., 10.1023/B:STUD.0000037125.49866.50, Stud. Log. 77 (2004), 153-180. (2004) Zbl1062.03062MR2080237DOI10.1023/B:STUD.0000037125.49866.50
- Boicescu, V., Filipoiu, A., Georgescu, G., Rudeanu, S., 10.1016/s0167-5060(08)x7005-0, Annals of Discrete Mathematics 49. North-Holland, Amsterdam (1991). (1991) Zbl0726.06007MR1112790DOI10.1016/s0167-5060(08)x7005-0
- Chang, C. C., 10.2307/1993227, Trans. Am. Math. Soc. 88 (1958), 467-490. (1958) Zbl0084.00704MR0094302DOI10.2307/1993227
- Chang,, C. C., 10.2307/1993423, Trans. Am. Math. Soc. 93 (1959), 74-80. (1959) Zbl0093.01104MR0122718DOI10.2307/1993423
- Cignoli, R., D'Ottaviano, I. M. L., Mundici, D., 10.1007/978-94-015-9480-6, Trends in Logic-Studia Logica Library 7. Kluwer Academic Publishers, Dordrecht (2000). (2000) Zbl0937.06009MR1786097DOI10.1007/978-94-015-9480-6
- Cignoli, R., Dubuc, E. J., Mundici, D., 10.1016/j.jpaa.2003.10.021, J. Pure Appl. Algebra 189 (2004), 37-59. (2004) Zbl1055.06004MR2038562DOI10.1016/j.jpaa.2003.10.021
- Cignoli, R., Marra, V., 10.1515/form.2011.109, Forum Math. 24 (2012), 1317-1331. (2012) Zbl1273.06006MR2996994DOI10.1515/form.2011.109
- Figallo, A. V., Algebras implicativas de Łukasiewicz -valuadas con diversas operaciones adicionales, Tesis Doctoral. Univ. Nac. del Sur (1990). (1990)
- Font, J. M., Rodríguez, A. J., Torrens, A., Wajsberg algebras, Stochastica 8 (1984), 5-31. (1984) Zbl0557.03040MR0780136
- Komori, Y., 10.1017/S0027763000018249, Nagoya Math. J. 72 (1978), 127-133. (1978) Zbl0363.02015MR0514894DOI10.1017/S0027763000018249
- Komori, Y., 10.1017/S0027763000019577, Nagoya Math. J. 84 (1981), 119-133. (1981) Zbl0482.03007MR0641149DOI10.1017/S0027763000019577
- Łukasiewicz, J., On three-valued logics, Ruch filozoficzny 5 (1920), 169-171 Polish. (1920)
- Łukasiewicz, J., Tarski, A., Untersuchungen über den Aussagenkalkül, C. R. Soc. Sc. Varsovie 23 (1930), 30-50. (1930) Zbl57.1319.01
- Martínez, N. G., 10.1007/BF00401552, Stud. Log. 49 (1990), 31-46. (1990) Zbl0717.03026MR1078437DOI10.1007/BF00401552
- Monteiro, L. F., Number of epimorphisms between finite Łukasiewicz algebras, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 49(97) (2006), 177-187. (2006) Zbl1150.03346MR2223313
- Rodríguez, A. J., Un studio algebraico de los cálculos proposicionales de Łukasiewicz, Ph. Doc. Diss. Universitat de Barcelona (1980). (1980)
- Rodríguez, A. J., Torrens, A., Verdú, V., Łukasiewicz logic and Wajsberg algebras, Bull. Sect. Log., Pol. Acad. Sci. 19 (1990), 51-55. (1990) Zbl0717.03027MR1077992
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.