Commutative algebra 2 (Rings, ideals, modules)
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. This lecture is a review of rings, ideals, and modules, where we give a few examples of non-commutative rings and rings without
From playlist Commutative algebra
Commutative algebra 53: Dimension Introductory survey
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 an introductory survey of many different ways of defining dimension. Reading: Section Exercises:
From playlist Commutative algebra
Commutative algebra 61: Examples of regular local rings
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 some examples of regular local rings. We first give an example of a regular local ring that is not geometrically regul
From playlist Commutative algebra
Commutative algebra 1 (Introduction)
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. https://link.springer.com/book/10.1007/978-1-4612-5350-1 This is a short introductory lecture, and gives a few examples of the
From playlist Commutative algebra
Definition of a Ring and Examples of Rings
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Ring and Examples of Rings - Definition of a Ring. - Definition of a commutative ring and a ring with identity. - Examples of Rings include: Z, Q, R, C under regular addition and multiplication The Ring of all n x
From playlist Abstract Algebra
Commutative algebra 60: Regular local rings
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 define regular local rings as the local rings whose dimension is equal to the dimension of their cotangent space. We give s
From playlist Commutative algebra
Abstract Algebra | Types of rings.
We define several and give examples of different types of rings which have additional structure. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Commutative algebra 5 (Noetherian rings)
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. In this lecture we find three equivalent ways of defining Noetherian rings, and give several examples of Noetherian and non-No
From playlist Commutative algebra
This lecture is part of an online course on rings and modules. We mainly discuss the problem of whether free modules over a ring have a well defined ran, generalizing the dimension of a vector space. We show that they do over many rings, including all non-zero commutative rings, but give
From playlist Rings and modules
What is a Tensor? Lesson 19: Algebraic Structures I
What is a Tensor? Lesson 19: Algebraic Structures Part One: Groupoids to Fields This is a redo or a recently posted lesson. Same content, a bit cleaner. Algebraic structures are frequently mentioned in the literature of general relativity, so it is good to understand the basic lexicon of
From playlist What is a Tensor?
This lecture is part of an online course on rings and modules. We discuss the operation of inverting the elements of a subset S of a ring R, called localization. We describe the localization in detail for commutative rings, and briefly discuss the non-commutative case. For the other lec
From playlist Rings and modules
Commutative algebra 12: Examples of Spec R
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 some examples of the spectrum of a ring, including the rings of Gaussian integers, polynomials and power series in 2 v
From playlist Commutative algebra
Commutative algebra 25 Artinian rings
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. In this lecture we show that Artinian rings are Noetherian, probably the trickiest result of the course. As an application we
From playlist Commutative algebra
On the long-term dynamics of nonlinear dispersive evolution equations - Wilhelm Schlag
Analysis Seminar Topic: On the long-term dynamics of nonlinear dispersive evolution equations Speaker: Wilhelm Schlag Affiliation: University of Chicago Visiting Professor, School of Mathematics Date: Febuary 14, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Commutative algebra 8 (Noetherian modules)
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. In this lecture we define Noetherian modules over a ring, and use the to prove Noether's theorem that the agerba of invariants
From playlist Commutative algebra
algebraic geometry 26 Affine algebraic sets and commutative rings
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between morphisms of affine algebraic sets and homomorphisms of commutative rings. As examples it describes some homomorphisms of commutative rings
From playlist Algebraic geometry I: Varieties