-ideals in pseudo-complemented distributive lattices
Archivum Mathematicum (2012)
- Volume: 048, Issue: 2, page 97-105
- ISSN: 0044-8753
Access Full Article
top
Abstract
topHow to cite
topSambasiva Rao, M.. "$\delta $-ideals in pseudo-complemented distributive lattices." Archivum Mathematicum 048.2 (2012): 97-105. <http://eudml.org/doc/246888>.
@article{SambasivaRao2012,
abstract = {The concept of $\delta $-ideals is introduced in a pseudo-complemented distributive lattice and some properties of these ideals are studied. Stone lattices are characterized in terms of $\delta $-ideals. A set of equivalent conditions is obtained to characterize a Boolean algebra in terms of $\delta $-ideals. Finally, some properties of $\delta $-ideals are studied with respect to homomorphisms and filter congruences.},
author = {Sambasiva Rao, M.},
journal = {Archivum Mathematicum},
keywords = {pseudo-complemented distributive lattice; dense element; closed element; $\delta $-ideal; Stone lattice; congruence; pseudocomplemented distributive lattice; dense element; closed element; -ideal; Stone lattice; Boolean algebra; congruence},
language = {eng},
number = {2},
pages = {97-105},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {$\delta $-ideals in pseudo-complemented distributive lattices},
url = {http://eudml.org/doc/246888},
volume = {048},
year = {2012},
}
TY - JOUR
AU - Sambasiva Rao, M.
TI - $\delta $-ideals in pseudo-complemented distributive lattices
JO - Archivum Mathematicum
PY - 2012
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 048
IS - 2
SP - 97
EP - 105
AB - The concept of $\delta $-ideals is introduced in a pseudo-complemented distributive lattice and some properties of these ideals are studied. Stone lattices are characterized in terms of $\delta $-ideals. A set of equivalent conditions is obtained to characterize a Boolean algebra in terms of $\delta $-ideals. Finally, some properties of $\delta $-ideals are studied with respect to homomorphisms and filter congruences.
LA - eng
KW - pseudo-complemented distributive lattice; dense element; closed element; $\delta $-ideal; Stone lattice; congruence; pseudocomplemented distributive lattice; dense element; closed element; -ideal; Stone lattice; Boolean algebra; congruence
UR - http://eudml.org/doc/246888
ER -
References
top- Balbes, R., Horn, A., Stone lattices, Duke Math. J. 37 (1970), 537–545. (1970) Zbl0207.02802MR0277448
- Birkhoff, G., Lattice Theory, Colloquium Publications, vol. 25, Amer. Math. Soc., New York, 1948. (1948) Zbl0033.10103MR0029876
- Cornish, W. H., 10.1017/S0004972700042404, Bull. Austral. Math. Soc. 8 (1973), 161–179. (1973) Zbl0251.06018MR0318024DOI10.1017/S0004972700042404
- Frink, O., 10.1215/S0012-7094-62-02951-4, Duke Math. J. 29 (1962), 505–514. (1962) Zbl0114.01602MR0140449DOI10.1215/S0012-7094-62-02951-4
- Grätzer, G., 10.1215/S0012-7094-63-03051-5, Duke Math. J. 30 (1963), 469–474. (1963) MR0153605DOI10.1215/S0012-7094-63-03051-5
- Grätzer, G., General lattice theory, Academic Press, New York, San Francisco, 1978. (1978) Zbl0436.06001MR0509213
- Speed, T. P., Two congruences on distributive lattices, Bull. Soc. Roy. Sci. Liège 38 (3–4) (1969), 86–95. (1969) Zbl0176.28504MR0245489
- Speed, T. P., 10.1017/S144678870001911X, J. Austral. Math. Soc. 18 (1974), 54–72. (1974) Zbl0294.06009MR0354476DOI10.1017/S144678870001911X
Citations in EuDML Documents
topNotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.