On the characterizations of complete distributive lattices by up-sets1

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-201430 ◽

2021 ◽

pp. 1-10

Author(s):

Peng He ◽

Xue-ping Wang

Keyword(s):

Distributive Lattice ◽

Distributive Lattices ◽

Algebraic Characterization ◽

Monotonic Operator

This paper first describes a characterization of a lattice L which can be represented as the collection of all up-sets of a poset. It then obtains a representation of a complete distributive lattice L0 which can be embedded into the lattice L such that all infima, suprema, the top and bottom elements are preserved under the embedding by defining a monotonic operator on a poset. This paper finally studies the algebraic characterization of a finite distributive.

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On the Partially Ordered Set of Prime Ideals of a Distributive Lattice

Canadian Journal of Mathematics ◽

10.4153/cjm-1971-097-3 ◽

1971 ◽

Vol 23 (5) ◽

pp. 866-874 ◽

Cited By ~ 10

Author(s):

Raymond Balbes

Keyword(s):

Distributive Lattice ◽

Partially Ordered Set ◽

Ordered Set ◽

Complete Characterization ◽

Distributive Lattices ◽

Prime Ideals ◽

Partially Ordered ◽

Irreducible Elements

For a distributive lattice L, let denote the poset of all prime ideals of L together with ∅ and L. This paper is concerned with the following type of problem. Given a class of distributive lattices, characterize all posets P for which for some . Such a poset P will be called representable over. For example, if is the class of all relatively complemented distributive lattices, then P is representable over if and only if P is a totally unordered poset with 0, 1 adjoined. One of our main results is a complete characterization of those posets P which are representable over the class of distributive lattices which are generated by their meet irreducible elements. The problem of determining which posets P are representable over the class of all distributive lattices appears to be very difficult.

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TOPOLOGICAL CHARACTERIZATION OF DUALLY NORMAL ALMOST DISTRIBUTIVE LATTICES

Asian-European Journal of Mathematics ◽

10.1142/s179355711250043x ◽

2012 ◽

Vol 05 (03) ◽

pp. 1250043

Author(s):

G. C. Rao ◽

N. Rafi ◽

Ravi Kumar Bandaru

Keyword(s):

Distributive Lattice ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Distributive Lattices ◽

Prime Ideals ◽

Topological Characterization ◽

Maximal Ideals ◽

Necessary And Sufficient

A dually normal almost distributive lattice is characterized topologically in terms of its maximal ideals and prime ideals. Some necessary and sufficient conditions for the space of maximal ideals to be dually normal are obtained.

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Characterization of BL-almost distributive lattices

Asian-European Journal of Mathematics ◽

10.1142/s1793557115500412 ◽

2015 ◽

Vol 08 (03) ◽

pp. 1550041 ◽

Cited By ~ 1

Author(s):

G. C. Rao ◽

Naveen Kumar Kakumanu

Keyword(s):

Distributive Lattice ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Distributive Lattices ◽

Necessary And Sufficient

Necessary and sufficient conditions for an Almost Distributive Lattice (ADL) to become a BL-ADL are derived. Different characterization of a BL-ADL are obtained. Relation between the operators on BL-ADL are derived. Wide choice of fundamental operations for a BL-ADL are derived.

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The Algebraic Characterization of Geometric 4-Manifolds

10.1017/cbo9780511526350 ◽

1994 ◽

Cited By ~ 14

Author(s):

J. A. Hillman

Keyword(s):

Algebraic Characterization

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Characterization of Dissipative Structures for First-Order Symmetric Hyperbolic System with General Relaxation

Mathematics ◽

10.3390/math9070728 ◽

2021 ◽

Vol 9 (7) ◽

pp. 728

Author(s):

Yasunori Maekawa ◽

Yoshihiro Ueda

Keyword(s):

Hyperbolic System ◽

Dissipative Structure ◽

Dissipative Structures ◽

Algebraic Characterization ◽

Symmetric Hyperbolic System ◽

Full Generality ◽

Order Linear ◽

First Order

In this paper, we study the dissipative structure of first-order linear symmetric hyperbolic system with general relaxation and provide the algebraic characterization for the uniform dissipativity up to order 1. Our result extends the classical Shizuta–Kawashima condition for the case of symmetric relaxation, with a full generality and optimality.

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An Axiomatic Characterization of a Class of Petri Nets

Fundamenta Informaticae ◽

10.3233/fi-1991-14405 ◽

1991 ◽

Vol 14 (4) ◽

pp. 477-491

Author(s):

Waldemar Korczynski

Keyword(s):

Petri Nets ◽

Petri Net ◽

Axiomatic Characterization ◽

Algebraic Characterization

In this paper an algebraic characterization of a class of Petri nets is given. The nets are characterized by a kind of algebras, which can be considered as a generalization of the concept of the case graph of a (marked) Petri net.

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Congruence relations on almost distributive lattices-II

Asian-European Journal of Mathematics ◽

10.1142/s1793557121500054 ◽

2019 ◽

pp. 2150005

Author(s):

Gezahagne Mulat Addis

Keyword(s):

Distributive Lattice ◽

Congruence Relation ◽

Congruence Class ◽

Distributive Lattices ◽

Ideal Formula ◽

Congruence Relations

For a given ideal [Formula: see text] of an almost distributive lattice [Formula: see text], we study the smallest and the largest congruence relation on [Formula: see text] having [Formula: see text] as a congruence class.

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