In this paper, we investigate the notion $\phi $-injectivity for Banach $ A $-modules, where
$\phi $ is a character on $ A. $ We obtain some hereditary properties of $\phi $-injectivity for …

We study the notions of φ-amenability and character amenability of the semigroup algebra l1
(S), where S is a semilattice. We also consider the character amenability of semigroup …

Let be a Banach algebra and let φ be a non-zero character on. We introduce and study the
notions φ-injectivity and φ-projectivity for Banach-modules ℰ by modifying the injectivity and …

In this paper, some homological notions of Banach A-modules such as ϕinjectivity, 0-
injectivity and character injectivity are discussed, where ϕ is a non-zero multiplicative linear …

In this paper, we study the notion of $\phi $-injectivity in the special case that $\phi= 0$. For
an arbitrary locally compact group $ G $, we characterize the 0-injectivity of $ L^{1}(G) $ as a …

Let S be a semigroup. In this paper we investigate the injectivity of ℓ1 (S) as a Banach right
module over ℓ1 (S). For weakly cancellative S this is the same as studying the flatness of the …

In this paper we study the relation between module amenability of θ-Lau product A× θ B and
that of Banach algebras A, B. We also discuss module biprojectivity of A× θ B. As a …

In this paper, we study the hereditary properties of module (𝜙, 𝜑)-amenability on Banach
algebras. We also define the concept of module character contractibility for Banach algebras …

In this paper we introduce the notion of module character amenable Banach algebras and
show that they possess module character virtual (approximate) diagonals. As a basic …

We shall study the χ-module Connes amenability of a semigroup algebra l 1 (S), where χ is a
bounded module homomorphism from l 1 (S) to l 1 (S) that is w∗-continuous and S is an …