Geodesic
Local bounded commutative residuated $\ell$-monoids
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 395-406 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Bounded commutative residuated lattice ordered monoids ($R\ell $-monoids) are a common generalization of, e.g., $BL$-algebras and Heyting algebras. In the paper, the properties of local and perfect bounded commutative $R\ell $-monoids are investigated.
Bounded commutative residuated lattice ordered monoids ($R\ell $-monoids) are a common generalization of, e.g., $BL$-algebras and Heyting algebras. In the paper, the properties of local and perfect bounded commutative $R\ell $-monoids are investigated.
Classification : 06D20, 06D35, 06F05, 06F35
Keywords: residuated $\ell $-monoid; residuated lattice; $BL$-algebra; $MV$-algebra; local $R\ell $-monoid; filter 
@article{CMJ_2007_57_1_a29,
     author = {Rach\r{u}nek, Ji\v{r}{\'\i} and \v{S}alounov\'a, Dana},
     title = {Local bounded commutative residuated $\ell$-monoids},
     journal = {Czechoslovak Mathematical Journal},
     pages = {395--406},
     year = {2007},
     volume = {57},
     number = {1},
     mrnumber = {2309973},
     zbl = {1174.06331},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a29/}
}
TY  - JOUR
AU  - Rachůnek, Jiří
AU  - Šalounová, Dana
TI  - Local bounded commutative residuated $\ell$-monoids
JO  - Czechoslovak Mathematical Journal
PY  - 2007
SP  - 395
EP  - 406
VL  - 57
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a29/
LA  - en
ID  - CMJ_2007_57_1_a29
ER  - 
%0 Journal Article
%A Rachůnek, Jiří
%A Šalounová, Dana
%T Local bounded commutative residuated $\ell$-monoids
%J Czechoslovak Mathematical Journal
%D 2007
%P 395-406
%V 57
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a29/
%G en
%F CMJ_2007_57_1_a29
Rachůnek, Jiří; Šalounová, Dana. Local bounded commutative residuated $\ell$-monoids. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 395-406. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a29/

[1] P.  Bahls, J.  Cole, N.  Galatos, P.  Jipsen, and C.  Tsinakis: Cancellative residuated lattices. Alg. Univ. 50 (2003), 83–106. | DOI | MR

[2] K.  Blount, C.  Tsinakis: The structure of residuated lattices. Intern. J.  Alg. Comp. 13 (2003), 437–461. | DOI | MR

[3] R. L. O.  Cignoli, I. M. L.  D’Ottaviano, and D. Mundici: Algebraic Foundations of Many-Valued Reasoning. Kluwer Acad. Publ., Dordrecht-Boston-London, 2000. | MR

[4] A.  Dvurečenskij, S.  Pulmannová: New Trends in Quantum Structures. Kluwer Acad. Publ., Dordrecht-Boston-London, 2000. | MR

[5] A.  Dvurečenskij, J.  Rachůnek: Probabilistic averaging in bounded residuated $\ell $-monoids. Semigroup Forum. 72 (2006), 191–206. | DOI | MR

[6] A.  Dvurečenskij, J.  Rachůnek: Bounded commutative residuated $\ell $-monoids with general comparability and states. Soft Comput. 10 (2006), 212–218. | DOI

[7] P.  Hájek: Metamathematics of Fuzzy Logic. Kluwer, Amsterdam, 1998. | MR

[8] P.  Jipsen, C.  Tsinakis: A survey of residuated lattices. In: Ordered Algebraic Structures, J.  Martinez (ed.), Kluwer Acad. Publ., Dordrecht, 2002, pp. 19–56. | MR

[9] J.  Rachůnek: $DR\ell $-semigroups and $MV$-algebras. Czechoslovak Math.  J. 48 (1998), 365–372. | DOI | MR

[10] J.  Rachůnek: $MV$-algebras are categorically equivalent to a class of  $DR\ell _{1(i)}$ semigroups. Math. Bohemica 123 (1998), 437–441. | MR

[11] J.  Rachůnek: A duality between algebras of basic logic and bounded representable $DR\ell $-monoids. Math. Bohemica 126 (2001), 561–569. | MR

[12] J.  Rachůnek, D.  Šalounová: Boolean deductive systems of bounded commutative residuated $\ell $-monoids. Contrib. Gen. Algebra 16 (2005), 199–207. | MR

[13] J.  Rachůnek, V.  Slezák: Negation in bounded commutative $DR\ell $-monoids. Czechoslovak Math.  J. 56 (2006), 755–763. | DOI | MR

[14] J.  Rachůnek, V.  Slezák: Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures. Math. Slovaca. 56 (2006), 223–233. | MR

[15] K. L. N.  Swamy: Dually residuated lattice ordered semigroups. Math. Ann. 159 (1965), 105–114. | DOI | MR | Zbl

[16] K. L. N. Swamy: Dually residuated lattice ordered semigroups  III. Math. Ann. 167 (1966), 71–74. | DOI | MR | Zbl

[17] E.  Turunen: Mathematics Behind Fuzzy Logic. Physica-Verlag, Heidelberg-New York, 1999. | MR | Zbl

[18] E.  Turunen, S.  Sessa: Local $BL$-algebras. Multip. Val. Logic 6 (2001), 229–250. | MR