Epimorphisms between finite MV-algebras

Aldo V. Figallo; Marina B. Lattanzi

Mathematica Bohemica (2017)

  • Volume: 142, Issue: 4, page 345-355
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Figallo, 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

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