Abstract algebra | Ideals (ring theory) | Ring theory
In the branch of abstract algebra known as ring theory, a minimal right ideal of a ring R is a nonzero right ideal which contains no other nonzero right ideal. Likewise, a minimal left ideal is a nonzero left ideal of R containing no other nonzero left ideals of R, and a minimal ideal of R is a nonzero ideal containing no other nonzero two-sided ideal of R . In other words, minimal right ideals are minimal elements of the poset of nonzero right ideals of R ordered by inclusion. The reader is cautioned that outside of this context, some posets of ideals may admit the zero ideal, and so the zero ideal could potentially be a minimal element in that poset. This is the case for the poset of prime ideals of a ring, which may include the zero ideal as a minimal prime ideal. (Wikipedia).
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
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
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
The Problem With Perfectionism
We aim for perfection without a correct idea of what perfection might demand from us. To strengthen our resolve, we need to improve our picture of what sacrifices any achievement will demand. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/p8kdj3 Join ou
From playlist SELF
From playlist Courses and Series
All Mathematicians are Minimalist
In this video I talk about why all mathematicians are actually minimalist, to some extent. Thoughts? Opinions? Leave a comment below:)
From playlist Cool Math Stuff
We are – almost all of us – deeply attracted to the idea of being normal. But what if our idea of ‘normal’ isn’t normal? A plea for a broader definition of an important term. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/ojRR53 Join our mailing list: h
From playlist SELF
Minimal logic, or minimal calculus, is an intuitionistic and paraconsistent logic, that rejects both the Law of Excluded Middle (LEM) as well as the Principle Of Explosion (Ex Falso Quodlibet, EFQ). https://en.wikipedia.org/wiki/Minimal_logic https://en.wikipedia.org/wiki/Principle_of_exp
From playlist Logic
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
MAG - Lecture 5 - Dickson's Lemma
metauni Algebraic Geometry (MAG) is a first course in algebraic geometry, in Roblox. In Lecture 5 we study monomial ideals and Dickson's Lemma, which says that any monomial ideal is finitely generated. The webpage for MAG is https://metauni.org/mag/. This video was recorded in The Rising
From playlist MAG
Commutative algebra 6 (Proof of Hilbert's basis 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. In this lecture we prove Hilbert's basis theorem that ideals of polynomial rings are finitely generated. We first do this by p
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
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
Idealness of k-wise intersecting families, by Tony Huynh
CMSA Combinatorics Seminar, 6 October 2020
From playlist CMSA Combinatorics Seminar
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
[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
The extreme homes of maximalists and minimalists - BBC REEL
In a world obsessed with clean, decluttered spaces, some people still find beauty in an overstuffed apartment. Live a better version of yourself with more stuff, or less? A maximalist and a minimalist, by showing us their lifestyle in extremes, confront each other on the relationship betw
From playlist Reel Ideas