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 $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A oplus E$, the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equipped with the algebras product $(a,x).(a^prime,x^prime)= (aa^prime, a.x^prime+ x.a^prime)$. In this paper, we investigate $triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$ with...