Engineering↗
Computing Ext Groups
Techniques for computing Ext: choice of variable, use of the long exact sequences, standard computations over the integers, and Ext for cyclic and finitely generated modules.
Tag
Ext and Tor
Every page in the KEVOS library tagged Ext and Tor. 7 pages.
Engineering↗
Extensions of Modules and the Baer Sum
Extensions of modules, equivalence of extensions, the Baer sum defined by pullback and pushout, and the resulting abelian group structure on Ext.
Engineering↗
The Ext Functor
Ext defined via extensions, via projective resolutions and via injective resolutions, the agreement of the three definitions, and the basic vanishing criteria.
Engineering↗
The Stein–Serre Theorem for Abelian Groups
The Stein-Serre theorem characterising countable torsion-free abelian groups that are free, via vanishing of Ext, and related Whitehead-type problems.
Engineering↗
The Tensor Product of Modules
The tensor product by universal property and construction, right exactness, flat modules, and the tensor-hom adjunction.
Engineering↗
The Tor Functor
Tor defined by projective resolutions, symmetry in its two variables, vanishing criteria, and the standard computations over the integers.
Engineering↗
The Two Long Exact Sequences of Ext
The long exact sequences of Ext in the first and second variables, their connecting homomorphisms, naturality, and the direction reversal caused by contravariance.
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