
Recent Posts
Archives
 May 2020
 April 2020
 March 2020
 June 2018
 July 2016
 June 2016
 May 2016
 March 2015
 February 2015
 January 2015
 December 2014
 December 2013
 November 2013
 July 2013
 June 2013
 May 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 April 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011
Categories
Meta
Pages
Tag Archives: exact sequences
Commutative Algebra 25
Arbitrary Collection of Modules Finally, we consider the case where we have potentially infinitely many modules. Proposition 1. For a collection of Amodules , we have Proof First claim: we will show that the LHS satisfies the universal property for … Continue reading
Posted in Advanced Algebra
Tagged direct products, direct sums, exact sequences, local properties, local rings, localization
Leave a comment
Commutative Algebra 21
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
Posted in Advanced Algebra
Tagged additive functors, exact sequences, functors, modules, short exact sequences
Leave a comment
Exact Sequences and the Grothendieck Group
As before, all rings are not commutative in general. Definition. An exact sequence of Rmodules is a collection of Rmodules and a sequence of Rmodule homomorphisms: such that for all i. Examples 1. The sequence is exact if and only if f … Continue reading
Posted in Notes
Tagged composition series, exact sequences, grothendieck group, modules, short exact sequences
Leave a comment