Martin Goldstern, Miroslav Ploščica (2002)
Discussiones Mathematicae - General Algebra and Applications
Similarity:
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.
Adam Grabowski (2013)
Formalized Mathematics
Similarity:
The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the Mizar Mathematical Library, there are some attempts to formalize prime ideals and filters; one series of articles written as decoding [9] proven some results; we tried however to follow [21], [12], and [13]. All three were devoted to the Stone representation theorem [18] for Boolean or Heyting lattices. The main aim of the present article...
Richard N. Ball, Aleš Pultr (2004)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Similarity:
Swamy, U.Maddana, Manikyamba, P. (1980)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Khalid A. Mokbel, Vilas S. Kharat (2013)
Mathematica Bohemica
Similarity:
Several characterizations of 0-distributive posets are obtained by using the prime ideals as well as the semiprime ideals. It is also proved that if every proper -filter of a poset is contained in a proper semiprime filter, then it is -distributive. Further, the concept of a semiatom in 0-distributive posets is introduced and characterized in terms of dual atoms and also in terms of maximal annihilator. Moreover, semiatomic 0-distributive posets are defined and characterized. It is...
Bozić, Milan (1980)
Publications de l'Institut Mathématique. Nouvelle Série
Similarity:
Radomír Halaš (1995)
Czechoslovak Mathematical Journal
Similarity:
M. Lambrou (1983)
Fundamenta Mathematicae
Similarity:
M. Sambasiva Rao (2012)
Archivum Mathematicum
Similarity:
The concept of -ideals is introduced in a pseudo-complemented distributive lattice and some properties of these ideals are studied. Stone lattices are characterized in terms of -ideals. A set of equivalent conditions is obtained to characterize a Boolean algebra in terms of -ideals. Finally, some properties of -ideals are studied with respect to homomorphisms and filter congruences.