Notes by Keith Conrad to follow along: https://kconrad.math.uconn.edu/blurbs/linmultialg/modulesoverPID.pdf
From playlist Abstract Algebra 2
Proof: Structure Theorem for Finitely Generated Torsion Modules Over a PID
This video has chapters to make the proof easier to follow. Splitting explanation: https://youtu.be/ZINtBNje_08 In this video we give a proof of the classification theorem using two smaller proofs by induction. We show both the elementary divisor form and the invariant factor form of a m
From playlist Ring & Module Theory
Lecture 22. Structure of finitely generated modules over PIDs and applications
Notes by Keith Conrad to follow along: https://kconrad.math.uconn.edu/blurbs/linmultialg/modulesoverPID.pdf
From playlist Abstract Algebra 2
Lecture 19. Structure of modules
From playlist Abstract Algebra 2
0:00 Motivation for studying modules 4:45 Definition of a vector space over a field 9:31 Definition of a module over a ring 12:12 Motivating example: structure of abelian groups 16:05 Motivating example: Jordan normal form 19:44 What unifies both examples (spoiler): Structure theorem for f
From playlist Abstract Algebra 2
Lecture 17. Isomorphism theorems. Free modules
0:00 0:19 1st isomorphism theorem 1:15 2nd isomorphism theorem 4:56 3rd isomorphism theorem 9:40 Submodules of a quotient module 12:55 Generators 18:34 Finitely generated modules 30:21 Cautionary example: not every submodule of a finitely generated module is finitely generated 33:18 Linea
From playlist Abstract Algebra 2
This lecture is part of an online course on rings and modules. We review basic properties of polynomials over a field, and show that polynomials in any number of variables over a field or the integers have unique factorization. For the other lectures in the course see https://www.youtu
From playlist Rings and modules
Lecture 18. Rank is well-defined
From playlist Abstract Algebra 2
Lecture 21. Aligned bases theorem
Notes by Keith Conrad to follow along: https://kconrad.math.uconn.edu/blurbs/linmultialg/modulesoverPID.pdf
From playlist Abstract Algebra 2
Abstract Algebra | Principal Ideals of a Ring
We define the notion of a principal ideal of a ring and give some examples. We also prove that all ideals of the integers are principal ideals, that is, the integers form a principal ideal domain (PID). http://www.michael-penn.net https://www.researchgate.net/profile/Michael_Penn5 http://
From playlist Abstract Algebra
Commutative algebra 28 Geometry of associated primes
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give a geometric interpretation of Ass(M), the set of associated primes of M, by showing that its closure is the support Su
From playlist Commutative algebra
From playlist Abstract Algebra 2
Jens Hemelaer: Toposes in arithmetic noncommutative geometry
Talk by Jens Hemelaer in Global Noncommutative Geometry Seminar (Americas) on February 5, 2021
From playlist Global Noncommutative Geometry Seminar (Americas)
Markus Land - L-Theory of rings via higher categories IV
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
John Coates: (1/4) Classical algebraic Iwasawa theory [AWS 2018]
slides for this lecture: http://swc-alpha.math.arizona.edu/video/2018/2018CoatesLecture1Slides.pdf lecture notes: http://swc.math.arizona.edu/aws/2018/2018CoatesNotes.pdf CLASSICAL ALGEBRAIC IWASAWA THEORY. JOHN COATES If one wants to learn Iwasawa theory, the starting point has to be t
From playlist Number Theory
Rings and modules 4 Unique factorization
This lecture is part of an online course on rings and modules. We discuss unique factorization in rings, showing the implications (Integers) implies (Euclidean domain) implies (Principal ideal domain) implies (Unique factorization domain). We give a few examples to illustrate these implic
From playlist Rings and modules
A Hecke action on the principal block of a semisimple algebraic group - Simon Riche
Workshop on Representation Theory and Geometry Topic: A Hecke action on the principal block of a semisimple algebraic group Speaker: Simon Riche Affiliation: Université Paris 6; Member, School of Mathematics Date: April 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Lecture 8. PIDs and Euclidean domains
From playlist Abstract Algebra 2