Balanced d-lattices are complemented
Martin Goldstern; Miroslav Ploščica
Discussiones Mathematicae - General Algebra and Applications (2002)
- Volume: 22, Issue: 1, page 33-37
- ISSN: 1509-9415
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topMartin Goldstern, and Miroslav Ploščica. "Balanced d-lattices are complemented." Discussiones Mathematicae - General Algebra and Applications 22.1 (2002): 33-37. <http://eudml.org/doc/287726>.
@article{MartinGoldstern2002,
abstract = {We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.},
author = {Martin Goldstern, Miroslav Ploščica},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {balanced congruence; balanced lattice; d-lattice; prime ideal; maximal ideal; -lattice},
language = {eng},
number = {1},
pages = {33-37},
title = {Balanced d-lattices are complemented},
url = {http://eudml.org/doc/287726},
volume = {22},
year = {2002},
}
TY - JOUR
AU - Martin Goldstern
AU - Miroslav Ploščica
TI - Balanced d-lattices are complemented
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2002
VL - 22
IS - 1
SP - 33
EP - 37
AB - We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.
LA - eng
KW - balanced congruence; balanced lattice; d-lattice; prime ideal; maximal ideal; -lattice
UR - http://eudml.org/doc/287726
ER -
References
top- [1] I. Chajda and G. Eigenthaler, Balanced congruences, Discuss. Math. - Gen. Algebra App. 21 (2001), 105-114.
- [2] G. Grätzer, General Lattice Theory (the second edition), Birkhäuser Verlag, Basel 1998.
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