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

Let M be a right R-module. We call M Rad-H-supplemented iffor each Y M there exists a direct summand D of M such that(Y + D)/D (Rad(M) + D)/D and (Y + D)/Y (Rad(M) + Y )/Y .It is shown that:(1) Let M = M1M2, where M1 is a fully invariant submodule of M.If M is Rad-H-supplemented, thenM1 andM2 are Rad-H-supplemented.(2) Let M = M1 M2 be a duo module and Rad--supplemented. IfM1 is radical M2-...