Kappa-Slender Modules

TL;DR

This paper introduces and studies new classes of modules called coordinatewise and tailwise -slender modules for any infinite cardinal , exploring their properties and related module classes.

Contribution

It defines and initiates the study of -slender modules for arbitrary infinite cardinals, expanding the theory of slender modules.

Findings

Defined coordinatewise -slender modules

Defined tailwise -slender modules

Explored properties of related classes of h-modules

Abstract

For an arbitrary infinite cardinal $\kappa$, we define classes of coordinatewise $\kappa$-slender and tailwise $\kappa$-slender modules as well as related classes of $h\kappa$-modules and initiate a study of these classes.