Displaying similar documents to “On the intersection of maximal filters in distributive lattices”

Balanced d-lattices are complemented

Martin Goldstern, Miroslav Ploščica (2002)

Discussiones Mathematicae - General Algebra and Applications

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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.

Prime Filters and Ideals in Distributive Lattices

Adam Grabowski (2013)

Formalized Mathematics

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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...

Coaxial filters of distributive lattices

M. Sambasiva Rao (2023)

Archivum Mathematicum

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Coaxial filters and strongly coaxial filters are introduced in distributive lattices and some characterization theorems of p m -lattices are given in terms of co-annihilators. Some properties of coaxial filters of distributive lattices are studied. The concept of normal prime filters is introduced and certain properties of coaxial filters are investigated. Some equivalent conditions are derived for the class of all strongly coaxial filters to become a sublattice of the filter lattice. ...

0-distributive posets

Khalid A. Mokbel, Vilas S. Kharat (2013)

Mathematica Bohemica

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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 l -filter of a poset is contained in a proper semiprime filter, then it is 0 -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...