Commuting Properties of Ext

Abstract

We characterize the abelian groups G for which the functors Ext(G, −) or Ext(−, G) commute with or invert certain direct sums or direct products.2010 Mathematics subject classification: primary 20K35; secondary 20K40.

When Ext Commutes With Direct Sums

“…Using this we first prove that G is an an extendible elementary p-group if and only if G is finite. This can be deduced from [S11,Theorem 5.3], but we include a proof for the reader's convenience.…”

The Defect Functor of a Homomorphism and Direct Unions

“…for general Grothendieck categories without enough projectives. For instance this equivalence is valid for the category of all Abelian p-groups (p is a fixed prime), which is a Grothendieck category without non-trivial projective objects, as a consequence of [31,Theorem 5.4].…”

“…This is based on the fact that Ext 1 R (M, −) commutes with respect to direct limits whenever M is an F P 2module, [19,Lemma 3.1.6]. In the case of Abelian groups, commuting properties of Ext 1 functors with respect particular direct limits were also studied in [4] and [31].…”

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

“…In [16] the authors provide an answer for abelian groups, and we refer to [8] for the case of contravariant Hom-functors. Other commuting properties of these functors, for the case of abelian groups, are studied in [3] and [21].…”