A cover-preserving embedding of semimodular lattices into geometric lattices

作者：Czedli Gabor^*; Schmidt E Tamas

来源：Advances in Mathematics, 2010, 225(5): 2455-2463.

DOI：10.1016/j.aim.2010.05.001

• Semimodular lattice
• Geometric lattice
• Cover-preserving embedding
• Matroid

Extending former results by G. Gratzer and E.W. Kiss (1986) [5] and M. Wild (1993) [9] on finite (upper) semimodular lattices, we prove that each semimodular lattice L of finite length has a cover-preserving embedding into a geometric lattice G of the same length. The number of atoms of our G equals the number of join-irreducible elements of L.

• 出版日期2010-12-1