Modules $M$ such that $\Ext_R^1(M,-)$ commutes with direct limits

TL;DR

This paper investigates the conditions under which the Ext^1 functor commutes with direct limits, utilizing Watts's theorem and Lenzing's characterization of finitely presented modules to deepen understanding of Ext-covariant functors.

Contribution

It introduces new criteria for modules M such that Ext^1_R(M, -) commutes with direct limits, connecting tensor functor properties with module finiteness.

Findings

Characterization of modules M with Ext^1_M(-) commuting with direct limits

Application of Watts's theorem to Ext-functor properties

Link between finitely presented modules and Ext-covariance

Abstract

We will use Watts's theorem together with Lenzing's characterization of finitely presented modules via commuting properties of the induced tensor functor in order to study commuting properties of Ext-covariant functors.