We survey some recent developments in understanding homological properties of finitely
generated modules over a complete intersection. These properties mainly concern with …

We introduce a class of local Noetherian rings, which we call minimal intersections, and
show that over such rings there exist classes of modules for which the derived functors Ext …

We start by surveying the tools of set–theoretic homological algebra that make it possible to
deconstruct roots of the contravariant Ext functor, ie., express them as transfinite extensions …

Modules M such that Ext R(M,−) Commutes with Direct Limits Page 1 Algebr Represent Theor
(2013) 16:1799–1808 DOI 10.1007/s10468-012-9382-y Modules M such that Ext 1 R(M,−) …

We show that if a class of modules is closed under pure quotients, then it is precovering if
and only if it is covering, and this happens if and only if it is closed under direct sums. This is …

In finitely cocomplete homological categories, co-smash products give rise to (possibly
higher-order) commutators of subobjects. We use binary and ternary co-smash products and …

The first section of this note is devoted to giving a unified proof of these results. This is
followed by showing that there exist abelian categories with an object C such that Ext'(C,.) …

We show that direct summands of certain additive functors arising as bifunctors with a fixed
argument in an abelian category are again of that form whenever the fixed argument has …

Following [3], in a category C with pullbacks and pushouts, we consider a full replete
subcategory C0, both reflective and coreflective in C, as the class of null objects in C …

A morphism f: M→ N of left R-modules is a phantom morphism if for any morphism g: A→ M,
with A finitely presented, the composition fg factors through a projective module …