Cofinitely (Weak) G-Supplemented Lattices
Abstract
In this work, cofinitely (weak) g-supplemented lattices are defined and some properties of these lattices are investigated. It is shown that quotient sublattices of cofinitely (weak) g-supplemented lattices are cofinitely (weak) g-supplemented. If 〖{a_i/0} 〗_(i∈I) is a collection of cofinitely (weak) g-supplemented sublattices of L and 1=⋁_(i∈I) a_i, then L is also cofinitely (weak) g-supplemented. It is proved that without loss of generality weak g-supplements of cofinite elements in compactly generated lattices are compact. An example showing that this is not true for lattices which are not cofinitely generated is given. A condition is given under which a compactly generated cofinitely weak g-supplemented lattice is cofinitely g-supplemented.
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References
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