… -free module M over an integral domain R is injective if and only … But as most injective modules
are not torsion-free, this … Another application of our results to prime characteristic algebra …

… character on A. We introduce and study the notions φ-injectivity and φ-projectivity for Banach
A-modules … φ-injectivity, φ-flatness and φ-projectivity of Banach A-modules by modifying the …

… and cotorsion modules, so-called Harmanci injective modules… among the concepts of injectivity,
flatness and cotorsionness. … of all modules whose character modules are Matlis injective …

… of n-flatness, viewed as generalizations of flatness; see[2, … regular if and only if all
modules are 1-injective. Indeed, for A … that all character modules of cyclic modules be 1-injective. …

… right R-modules are finitely presented. As compared to considerinq flatness of products of a
… paper investigates flatness (and related properties) of products of an injective cogenerator. …

… left coherent (and right perfect) rings, left Noetherian rings and left Artinian rings in terms
of the C-(FP-)injectivity, flatness and projectivity of character modules of certain left S-modules. …

… module M is rugged if and only if the character right module M … right module is poor or injective
if and only if every left module … module is the same as the injectivity domain of its character …

… Artinian rings by the flatness, projectivity, and injectivity of the character module of certain left
R-… remaining condition: A module is injective if and only if its character module is projective. …

… First, we recall some standard notations that we shall use and define the notions of φ-injectivity
and φ-flatness of Banach modules. Let A be a Banach algebra and E ∈ A-mod. …

… , 1)-injective, then each (1, 1)-flat right R-module is projective. For many classes of rings, for
each positive integer p, we show that the (1, p)-flatness implies the (ℵ 0 , p)-flatness, but we …