scholarly journals Tight embedding of modular lattices into partition lattices: progress and program

2018 ◽  
Vol 79 (4) ◽  
Author(s):  
Marcel Wild
Keyword(s):  
Modular Lattices ◽  
Partition Lattices

scholarly journals Seven-modular lattices and a septic base Jacobi identity

2003 ◽  
Vol 99 (2) ◽  
pp. 361-372 ◽  
Author(s):  
Heng Huat Chan ◽  
Kok Seng Chua ◽  
Patrick Solé
Keyword(s):  
Jacobi Identity ◽  
Modular Lattices

Matchings and Radon transforms in lattices II. Concordant sets

1987 ◽  
Vol 101 (2) ◽  
pp. 221-231 ◽  
Author(s):  
Joseph P. S. Kung
Keyword(s):  
Incidence Matrix ◽  
Finite Lattice ◽  
Möbius Function ◽  
Radon Transforms ◽  
Modular Lattices ◽  
Covering Theorem ◽  
Mobius Function ◽  
Finite Lattices ◽  
Semimodular Lattices

AbstractLet and ℳ be subsets of a finite lattice L. is said to be concordant with ℳ if, for every element x in L, either x is in ℳ or there exists an element x+ such that (CS1) the Möbius function μ(x, x+) ≠ 0 and (CS2) for every element j in , x ∨ j ≠ x+. We prove that if is concordant with ℳ, then the incidence matrix I(ℳ | ) has maximum possible rank ||, and hence there exists an injection σ: → ℳ such that σ(j) ≥ j for all j in . Using this, we derive several rank and covering inequalities in finite lattices. Among the results are generalizations of the Dowling-Wilson inequalities and Dilworth's covering theorem to semimodular lattices, and a refinement of Dilworth's covering theorem for modular lattices.

Algebraic Aspects of Partition Lattices

1992 ◽  
pp. 106-122 ◽  
Author(s):  
Ivan Rival ◽  
Miriam Stanford
Keyword(s):  
Partition Lattices

scholarly journals Baer-Galois connections and applications

2014 ◽  
Vol 30 (2) ◽  
pp. 225-229
Author(s):  
GABRIELA OLTEANU ◽  
Keyword(s):  
Modular Lattices ◽  
Galois Connections ◽  
Baer Modules

We define Baer-Galois connections between bounded modular lattices. We relate them to lifting lattices and we show that they unify the theories of (relatively) Baer and dual Baer modules.

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