Spectral topologies of dually residuated lattice-ordered monoids
Mathematica Bohemica, Tome 129 (2004) no. 4, pp. 379-391

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
Dually residuated lattice-ordered monoids ($DR\ell $-monoids for short) generalize lattice-ordered groups and include for instance also $GMV$-algebras (pseudo $MV$-algebras), a non-commutative extension of $MV$-algebras. In the present paper, the spectral topology of proper prime ideals is introduced and studied.
Dually residuated lattice-ordered monoids ($DR\ell $-monoids for short) generalize lattice-ordered groups and include for instance also $GMV$-algebras (pseudo $MV$-algebras), a non-commutative extension of $MV$-algebras. In the present paper, the spectral topology of proper prime ideals is introduced and studied.
DOI : 10.21136/MB.2004.134046
Classification : 03G10, 03G25, 06D35, 06F05
Keywords: $DR\ell $-monoid; prime ideal; spectrum
Kühr, Jan. Spectral topologies of dually residuated lattice-ordered monoids. Mathematica Bohemica, Tome 129 (2004) no. 4, pp. 379-391. doi: 10.21136/MB.2004.134046
@article{10_21136_MB_2004_134046,
     author = {K\"uhr, Jan},
     title = {Spectral topologies of dually residuated lattice-ordered monoids},
     journal = {Mathematica Bohemica},
     pages = {379--391},
     year = {2004},
     volume = {129},
     number = {4},
     doi = {10.21136/MB.2004.134046},
     mrnumber = {2102611},
     zbl = {1080.06023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2004.134046/}
}
TY  - JOUR
AU  - Kühr, Jan
TI  - Spectral topologies of dually residuated lattice-ordered monoids
JO  - Mathematica Bohemica
PY  - 2004
SP  - 379
EP  - 391
VL  - 129
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2004.134046/
DO  - 10.21136/MB.2004.134046
LA  - en
ID  - 10_21136_MB_2004_134046
ER  - 
%0 Journal Article
%A Kühr, Jan
%T Spectral topologies of dually residuated lattice-ordered monoids
%J Mathematica Bohemica
%D 2004
%P 379-391
%V 129
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2004.134046/
%R 10.21136/MB.2004.134046
%G en
%F 10_21136_MB_2004_134046

[1] R. Balbes, P. Dwinger: Distributive Lattices. University of Missouri Press, Columbia, 1974. | MR

[2] R. L. O. Cignoli, I. M. L. D’Ottawiano, D. Mundici: Algebraic Foundations of Many-Valued Reasoning. Kluwer, Dordrecht, 2000.

[3] A. Di Nola, G. Georgescu, A. Iorgulescu: Pseudo $BL$-algebras: Part I. Mult. Valued Log. 8 (2002), 673–714. | MR

[4] A. Di Nola, G. Georgescu, A. Iorgulescu: Pseudo $BL$-algebras: Part II. Mult. Valued Log. 8 (2002), 717–750. | MR

[5] R. Engelking: General Topology. PWN, Warszawa, 1977. | MR | Zbl

[6] G. Georgescu, A. Iorgulescu: Pseudo $MV$-algebras. Mult. Valued Log. 6 (2001), 95–135. | MR

[7] A. M. W. Glass: Partially Ordered Groups. World Scientific, Singapore, 1999. | MR | Zbl

[8] P. Hájek: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht, 1998. | MR

[9] P. Hájek: Basic fuzzy logic and $BL$-algebras. Soft Comput. 2 (1998), 124–128. | DOI

[10] T. Kovář: A General Theory of Dually Residuated Lattice Ordered Monoids. Ph.D. Thesis, Palacký Univ., Olomouc, 1996.

[11] J. Kühr: Ideals of non-commutative $DR\ell $-monoids. (to appear).

[12] J. Kühr: Prime ideals and polars in $DR\ell $-monoids and pseudo $BL$-algebras. Math. Slovaca 53 (2003), 233–246. | MR

[13] J. Rachůnek: Spectra of autometrized lattice algebras. Math. Bohem. 123 (1998), 87–94. | MR

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

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

[16] J. Rachůnek: A non-commutative generalization of $MV$-algebras. Czechoslovak Math. J. 52 (2002), 255–273. | DOI | MR | Zbl

[17] J. Rachůnek: Prime spectra of non-commutative generalizations of $MV$-algebras. Algebra Univers. 48 (2002), 151–169. | DOI | MR | Zbl

[18] J. T. Snodgrass, C. Tsinakis: Finite-valued algebraic lattices. Algebra Univers. 30 (1993), 311–318. | MR

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

Cité par Sources :