g-Supplemented lattices

[摘要] In this work, g-supplemented lattices are defined and some properties of these lattices are investigated. g-small submodules and g-supplemented modules are generalized to lattices. Let L be a lattice and 1 = a1 ∨a2 ∨...∨an with ai ∈ L (1 ≤ i ≤ n). If ai/0 is g-supplemented for every i = 1,2,...,n, then L is also g-supplemented. If L is g-supplemented, then 1/a is also g-supplemented for every a ∈ L. It is also defined the g-radical of a lattice L and it is shown that if L is g-supplemented, then 1/rg (L) is complemented.

[学科分类] 数学（综合）

[关键词] Lattices;Essential Elements;Small Elements;Supplemented Lattices