Mathematicae General Algebra and Applications 22(1) (2002) 33-37
BALANCED d-LATTICES ARE COMPLEMENTED
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.
Keywords: balanced congruence, balanced lattice, d-lattice, prime ideal, maximal ideal.
2000 AMS Mathematics Subject Classifications: 06B10, 08A30.
I. Chajda and G. Eigenthaler, Balanced congruences, Discuss. Math. - Gen. Algebra App. 21
G. Grätzer, General Lattice Theory (the second edition), Birkhäuser Verlag, Basel 1998.
Received 3 December 2001