Abstract Algebra | Maximal and prime ideals.
We prove some classic results involving maximal and prime ideals. Specifically we prove the an ideal P is prime iff R/P is an integral domain. Further, we prove that an ideal M is maximal iff R/M is a field. http://www.michael-penn.net https://www.researchgate.net/profile/Michael_Penn5 ht
From playlist Abstract Algebra
Interesting Facts About the Last Digits of Prime Numbers
This video explains some interesting facts about the last digits of prime numbers.
From playlist Mathematics General Interest
This is Why Minimalism is a Thing
In this video I talk about why minimalism is a thing people follow in today's society. There is a reason, and it's a good one.
From playlist Inspiration and Life Advice
Every Nonzero Prime Ideal in a Principal Ideal Domain is Maximal Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Every Nonzero Prime Ideal in a Principal Ideal Domain is Maximal Proof
From playlist Abstract Algebra
Maximum and Minimum of a set In this video, I define the maximum and minimum of a set, and show that they don't always exist. Enjoy! Check out my Real Numbers Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCZggpJZvUXnUzaw7fHCtoh
From playlist Real Numbers
Proof: Prime Ideals are Maximal in a PID
In a principal ideal domain, if an ideal is a prime ideal, that implies it is a maximal ideal, as long as it is not just the zero ideal. Here we give a straightforward explanation of this theorem from ring theory! Ring & Module Theory playlist: https://www.youtube.com/playlist?list=PLug5Z
From playlist Ring & Module Theory
Maximum and Minimum Values (Closed interval method)
A review of techniques for finding local and absolute extremes, including an application of the closed interval method
From playlist 241Fall13Ex3
Rings 6 Prime and maximal ideals
This lecture is part of an online course on rings and modules. We discuss prime and maximal ideals of a (commutative) ring, use them to construct the spectrum of a ring, and give a few examples. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj5
From playlist Rings and modules
I is a Maximal Ideal iff R/I is a Field Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys I is a Maximal Ideal iff R/I is a Field Proof
From playlist Abstract Algebra
Nonlinear algebra, Lecture 12: "Primary Decomposition ", by Mateusz Michalek and Bernd Sturmfels
This is the twelth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Algebraic geometry 51: Bezout's theorem
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. The lectures continue in the playlist "scheme theory". It is about Bezout's theorem and its variations, which say that under some conditions the degree of an intersecti
From playlist Algebraic geometry I: Varieties
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
Nonlinear algebra, Lecture 1: "Polynomials, Ideals, and Groebner Bases", by Bernd Sturmfels
This is the first lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences. Topics covered: polynomilas, ideals and Groebner bases.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
[ANT13] Dedekind domains, integral closure, discriminants... and some other loose ends
In this video, we see an example of how badly this theory can fail in a non-Dedekind domain, and so - regrettably - we finally break our vow of not learning what a Dedekind domain is.
From playlist [ANT] An unorthodox introduction to algebraic number theory
Commutative algebra 15 (Noetherian spaces)
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 topological spaces, and use them to show that for a Noetherian ring R, every closed subse
From playlist Commutative algebra
Elliptic Curves - Lecture 18a - Elliptic curves over local fields (the fundamental exact sequence)
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
How to Find a Minimal Generating Set
How to Find a Minimal Generating Set
From playlist Linear Algebra
Commutative algebra 59: Krull's principal ideal theorem
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 applications of the theorems we proved about the dimension of local rings. We first show that the dimension of a
From playlist Commutative algebra