Baer-Galois connections and applications

GABRIELA OLTEANU;

doi:10.37193/cjm.2014.02.06

Baer-Galois connections and applications

Carpathian Journal of Mathematics ◽

10.37193/cjm.2014.02.06 ◽

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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Seven-modular lattices and a septic base Jacobi identity

Journal of Number Theory ◽

10.1016/s0022-314x(02)00069-0 ◽

2003 ◽

Vol 99 (2) ◽

pp. 361-372 ◽

Cited By ~ 5

Author(s):

Heng Huat Chan ◽

Kok Seng Chua ◽

Patrick Solé

Keyword(s):

Jacobi Identity ◽

Modular Lattices

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Fuzzy Galois connections on fuzzy sets

Fuzzy Sets and Systems ◽

10.1016/j.fss.2018.05.016 ◽

2018 ◽

Vol 352 ◽

pp. 26-55 ◽

Cited By ~ 5

Author(s):

Javier Gutiérrez García ◽

Hongliang Lai ◽

Lili Shen

Keyword(s):

Fuzzy Sets ◽

Galois Connections

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Matchings and Radon transforms in lattices II. Concordant sets

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100066573 ◽

1987 ◽

Vol 101 (2) ◽

pp. 221-231 ◽

Cited By ~ 6

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.

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