Tag Archives: exact sequences

Commutative Algebra 25

Posted on April 12, 2020 by limsup

Arbitrary Collection of Modules Finally, we consider the case where we have potentially infinitely many modules. Proposition 1. For a collection of A-modules , we have Proof First claim: we will show that the LHS satisfies the universal property for … Continue reading →

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Commutative Algebra 21

Posted on April 8, 2020 by limsup

Exact Sequences When studying homomorphisms of modules over a fixed ring, we often encounter sequences like this: where each is a homomorphism of modules. This sequence may terminate (on either end) or it may continue indefinitely. Note on indices: usually … Continue reading →

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Exact Sequences and the Grothendieck Group

Posted on January 20, 2015 by limsup

As before, all rings are not commutative in general. Definition. An exact sequence of R-modules is a collection of R-modules and a sequence of R-module homomorphisms: such that for all i. Examples 1. The sequence is exact if and only if f … Continue reading →

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