Geodesic
Characterizations of the $0$-distributive semilattice
Mathematica Bohemica, Tome 128 (2003) no. 3, pp. 237-252

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

MR Zbl
The $0$-distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for $0$-distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.
The $0$-distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for $0$-distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.
DOI : 10.21136/MB.2003.134177
Classification : 06A12, 06A99, 06B10, 06B99
Keywords: semilattice; prime ideal; filter 
Balasubramani, P. Characterizations of the $0$-distributive semilattice. Mathematica Bohemica, Tome 128 (2003) no. 3, pp. 237-252. doi: 10.21136/MB.2003.134177
@article{10_21136_MB_2003_134177,
     author = {Balasubramani, P.},
     title = {Characterizations of the $0$-distributive semilattice},
     journal = {Mathematica Bohemica},
     pages = {237--252},
     year = {2003},
     volume = {128},
     number = {3},
     doi = {10.21136/MB.2003.134177},
     mrnumber = {2012602},
     zbl = {1052.06002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134177/}
}
TY  - JOUR
AU  - Balasubramani, P.
TI  - Characterizations of the $0$-distributive semilattice
JO  - Mathematica Bohemica
PY  - 2003
SP  - 237
EP  - 252
VL  - 128
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134177/
DO  - 10.21136/MB.2003.134177
LA  - en
ID  - 10_21136_MB_2003_134177
ER  - 
%0 Journal Article
%A Balasubramani, P.
%T Characterizations of the $0$-distributive semilattice
%J Mathematica Bohemica
%D 2003
%P 237-252
%V 128
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134177/
%R 10.21136/MB.2003.134177
%G en
%F 10_21136_MB_2003_134177

[1] P. Balasubramani, P. V. Venkatanarasimhan: Characterizations of the $0$-distributive lattice. J. Pure Appl. Math. 32 (2001), 315–324. | MR

[2] G. Grätzer: Lattice Theory First Concepts and Distributive Lattices. W. H. Freeman, San Francisco, 1971. | MR

[3] C. Jayaram: Prime $\alpha $-ideals in a $0$-distributive lattice. J. Pure Appl. Math. 17 (1986), 331–337. | MR | Zbl

[4] Y. S. Pawar, N. K. Thakare: $0$-distributive semilattices. Canad. Math. Bull. 21 (1978), 469–475. | DOI | MR

[5] Y. S. Pawar, N. K. Thakare: Minimal prime ideals in $0$-distributive lattices. Period. Math. Hungar. 13 (1982), 237–246. | DOI | MR

[6] G. Szasz: Introduction to Lattice Theory. Academic Press, New York, 1963. | MR

[7] J. Varlet: A generalization of the notion of pseudocomplementedness. Bull. Soc. Roy. Sci. Liege 37 (1968), 149–158. | MR

[8] J. Varlet: Distributive semilattices and Boolean lattices. Bull. Soc. Roy. Liege 41 (1972), 5–10. | MR | Zbl

[9] P. V. Venkatanarasimhan: Pseudocomplements in posets. Proc. Amer. Math. Soc. 28 (1971), 9–17. | DOI | MR

[10] P. V. Venkatanarasimhan: Semiideals in semilattices. Col. Math. 30 (1974), 203–212.

Cité par Sources :