Pseudo-complements in semi-lattices

Frink, Orrin

doi:10.1215/s0012-7094-62-02951-4

Cited by 144 publications

(91 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Our next result is an extension of some results of J. Varlet [11] and O. Frink [4]. More precisely II is a generalisation of the condition II => III.…”

Section: More General Characterisations Of Stone Latticessupporting

confidence: 60%

See 1 more Smart Citation

On Stone Lattices

Speed

1969

J. Aust. Math. Soc.

View full text Add to dashboard Cite

M. H. Stone raised the problem ([1] Problem 70) of characterising the class of distributive pseudo-complemented lattices ℒ = 〈L; ∨, ∧, 0, 1〉 in which a* ∨ a** = 1 holds identically. Several solutions to this problem have now been offered — the first being by G. Grätzer and E. T. Schmidt [6], who gave this class of lattices the name Stone lattices. Later solutions were given by J. Varlet [11], O. Frink [4] and G. Grätzer [5]; see also G. Bruns [2].

show abstract

“…Our next result is an extension of some results of J. Varlet [11] and O. Frink [4]. More precisely II is a generalisation of the condition II => III.…”

Section: More General Characterisations Of Stone Latticessupporting

confidence: 60%

“…We have shown (a) is dense and the Lemma is proved. G. Gratzer [5] proved the following result, after a conjecture of O. Frink [4]. See also G. Bruns [2].…”

Section: Let 3? = (L; V a 0 1> Be A Stone Lattice Then For A E (Amentioning

confidence: 80%

On Stone Lattices

Speed

1969

J. Aust. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…We recall a basic structure result for pseudo-complemented complete lattices (Glivenko [8], Frink [6]). …”

Section: Using the Structure Of Pseudo-complemented Latticesmentioning

confidence: 99%

The Jónsson-Kiefer Property

et al. 2006

View full text Add to dashboard Cite

Abstract. The least element 0 of a finite meet semi-distributive lattice is a meet of meet-prime elements. We investigate conditions under which the least element of an algebraic, meet semi-distributive lattice is a (complete) meet of meet-prime elements. For example, this is true if the lattice has only countably many compact elements, or if |L| < 2 ℵ 0 , or if L is in the variety generated by a finite meet semi-distributive lattice. We give an example of an algebraic, meet semi-distributive lattice that has no meet-prime element or join-prime element. This lattice L has |L| = |Lc| = 2 ℵ 0 where Lc is the set of compact elements of L.

show abstract

“…It is well known (cf. [5]) that the set B(S) of closed elements a (i.e., a = a**) of S is a Boolean algebra whose meet and complement operations are respectively the meet and * in S and whose join operation V is given by a\J b = (a* /\b*)*.…”

mentioning

confidence: 99%