On character projectivity Of Banach modules

Let $A$ be a Banach algebra, $\Omega(A)$ be the character space of $A$ and $\alpha\in\Omega(A)$. In this paper, we examine the characteristics of $\alpha$-projective (injective) $A$-modules and demonstrate that these character-based $A$-modules also satisfy well-known classical homological properties on Banach $A$-modules.

Keywords:

‎Banach algebra‎ , ‎$A$‎- ‎module‎ , ‎Banach $A$‎- ‎module‎ , ‎projective and injective modules