Geodesic
Epimorphisms between finite MV-algebras
Mathematica Bohemica, Tome 142 (2017) no. 4, pp. 345-355 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/MB.2017.0077-14
Classification : 06D35, 08A35
Keywords: MV-algebras; mv-function; epimorphism 
@article{10_21136_MB_2017_0077_14,
     author = {Figallo, Aldo V. and Lattanzi, Marina B.},
     title = {Epimorphisms between finite {MV-algebras}},
     journal = {Mathematica Bohemica},
     pages = {345--355},
     year = {2017},
     volume = {142},
     number = {4},
     doi = {10.21136/MB.2017.0077-14},
     mrnumber = {3739022},
     zbl = {06819590},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0077-14/}
}
TY  - JOUR
AU  - Figallo, Aldo V.
AU  - Lattanzi, Marina B.
TI  - Epimorphisms between finite MV-algebras
JO  - Mathematica Bohemica
PY  - 2017
SP  - 345
EP  - 355
VL  - 142
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0077-14/
DO  - 10.21136/MB.2017.0077-14
LA  - en
ID  - 10_21136_MB_2017_0077_14
ER  - 
%0 Journal Article
%A Figallo, Aldo V.
%A Lattanzi, Marina B.
%T Epimorphisms between finite MV-algebras
%J Mathematica Bohemica
%D 2017
%P 345-355
%V 142
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0077-14/
%R 10.21136/MB.2017.0077-14
%G en
%F 10_21136_MB_2017_0077_14
Figallo, Aldo V.; Lattanzi, Marina B. Epimorphisms between finite MV-algebras. Mathematica Bohemica, Tome 142 (2017) no. 4, pp. 345-355. doi: 10.21136/MB.2017.0077-14

Cité par Sources :