Geodesic
On a certain construction of lattice expansions
Mathematica Bohemica, Tome 129 (2004) no. 1, pp. 1-9

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

MR Zbl
We obtain a simple construction for particular subclasses of several varieties of lattice expansions. The construction allows a unified approach to the characterization of the subdirectly irreducible algebras
We obtain a simple construction for particular subclasses of several varieties of lattice expansions. The construction allows a unified approach to the characterization of the subdirectly irreducible algebras
DOI : 10.21136/MB.2004.134105
Classification : 06D05, 08B26
Keywords: lattice expansions; subdirectly irreducibles; triples 
Gramaglia, Hector. On a certain construction of lattice expansions. Mathematica Bohemica, Tome 129 (2004) no. 1, pp. 1-9. doi: 10.21136/MB.2004.134105
@article{10_21136_MB_2004_134105,
     author = {Gramaglia, Hector},
     title = {On a certain construction of lattice expansions},
     journal = {Mathematica Bohemica},
     pages = {1--9},
     year = {2004},
     volume = {129},
     number = {1},
     doi = {10.21136/MB.2004.134105},
     mrnumber = {2048782},
     zbl = {1052.06008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2004.134105/}
}
TY  - JOUR
AU  - Gramaglia, Hector
TI  - On a certain construction of lattice expansions
JO  - Mathematica Bohemica
PY  - 2004
SP  - 1
EP  - 9
VL  - 129
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2004.134105/
DO  - 10.21136/MB.2004.134105
LA  - en
ID  - 10_21136_MB_2004_134105
ER  - 
%0 Journal Article
%A Gramaglia, Hector
%T On a certain construction of lattice expansions
%J Mathematica Bohemica
%D 2004
%P 1-9
%V 129
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2004.134105/
%R 10.21136/MB.2004.134105
%G en
%F 10_21136_MB_2004_134105

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

[2] J. Berman: Distributive lattices with an additional operation. Aequationes Math. 16 (1977), 321–331. | MR

[3] T. S. Blyth, J. C. Varlet: On a common abstraction of De Morgan algebras and Stone algebras. Proc. Roy. Soc. Edinburgh Sect. A 94 (1983), 301–308. | MR

[4] T. S. Blyth, J. C. Varlet: Subvarieties of the class of $MS$-algebras. Proc. Roy. Soc. Edinburgh Sect. A 94 (1983), 157–169. | MR

[5] C. Chen, G. Grätzer: Stone lattices I, Construction theorems. Can. J. Math. 21 (1969), 884–894. | DOI | MR

[6] H. Gramaglia, D. Vaggione: (Finitely) Subdirectly irreducibles and Birkhoff-like sheaf representation for certain varieties of lattice ordered structures. Algebra Universalis 38 (1997), 56–91. | DOI | MR

[7] G. Grätzer: General Lattice Theory, second edition. Birkhäuser, Berlin, 1998. | MR

[8] M. Haviar: On certain construction of MS-algebras. Port. Math. 51 (1994), 71–83. | MR

[9] D. Hobby: Semi-De Morgan algebras. Studia Logica 56 (1996), 151–183. | DOI | MR | Zbl

[10] T. Katriňák: Über eine Konstruktion der distributiven pseudokomplementaren Halverbände. J. Reine Angew. Math. 241 (1969), 160–174.

[11] T. Katriňák, P. Mederly: Construction of $p$-algebras. Algebra Universalis 17 (1983), 288–316. | DOI

[12] T. Katriňák, K. Mikula: On construction of MS-algebras. Port. Math. 45 (1988), 157–163. | MR

[13] H. Lakser: The structure of pseudo-complemented distributive lattices I: subdirect decomposition. Trans. Amer. Math. Soc. 156 (1971), 335–342. | MR

[14] H. Sankappanavar: Demi-pseudocomplemented lattices: principal congruences and subdirect irreducibility. Algebra Universalis 27 (1990), 180–193. | DOI | MR | Zbl

[15] H. Sankappanavar: Semi-De Morgan algebras. J. Symbolic Logic 52 (1987), 712–724. | DOI | MR | Zbl

Cité par Sources :