Commutative algebra | Module theory
In the context of a module M over a ring R, the top of M is the largest semisimple quotient module of M if it exists. For finite-dimensional k-algebras (k a field) R, if rad(M) denotes the intersection of all proper maximal submodules of M (the radical of the module), then the top of M is M/rad(M). In the case of local rings with maximal ideal P, the top of M is M/PM. In general if R is a semilocal ring (=semi-artinian ring), that is, if R/Rad(R) is an Artinian ring, where Rad(R) is the Jacobson radical of R, then M/rad(M) is a semisimple module and is the top of M. This includes the cases of local rings and finite dimensional algebras over fields. (Wikipedia).
Topoi 3: The definition of a topos
This is video number 3 in the series defining topoi. Here's the updated text used in the video: https://gist.github.com/Nikolaj-K/469b9ca1c085ea4ac4e3d7d0008913f5 Fourth video on Power and Negation in a topos: https://youtu.be/dvXRQI8RonY
From playlist Algebra
Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
Algebra for beginners || Basics of Algebra
In this course you will learn about algebra which is ideal for absolute beginners. #Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like
From playlist Algebra
Algebra - Ch. 4: Exponents & Scientific Notation (1 of 35) What is an Exponent?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is an exponent. A number or symbol placed above another number or symbol that indicates the power the number or symbol at the bottom is raised. The number at the bottom is called the base
From playlist ALGEBRA CH 4 EXPONENTS AND SCIENTIFIC NOTATION
Algebra is one of the broad areas of mathematics, together with number theory, geometry and analysis. In its most general form, #algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. In this course
From playlist Algebra
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
As part of the college algebra series, this Center of Math video will teach you the basics of functions, including how they're written and what they do.
From playlist Basics: College Algebra
How to Be Successful In Algebra
TabletClass Math: https://tcmathacademy.com/ This video explains how to be successful in algebra – this will help you not only to pass your algebra class but to get a top grade in algebra.
From playlist Algebra
Monica Vazirani: Representations of the affine BMW category
The BMW algebra is a deformation of the Brauer algebra, and has the Hecke algebra of type A as a quotient. Its specializations play a role in types B, C, D akin to that of the symmetric group in Schur-Weyl duality. I will discuss Walker’s TQFT-motivated 1-handle construction of a family of
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Algebraic Fractions - Cancelling (L1) Core 3 Edexcel A-Level
Powered by https://www.numerise.com/ This video is a tutorial on Cancelling Algebraic Fractions for Core 3 Math A-Level. Please make yourself revision notes while watching this and attempt my examples. Complete the suggested exercises from the Edexcel book. After this then move to my ne
From playlist Core 3: Edexcel A-Level Maths Full Course
Lukas NABERGALL - Tree-like Equations from the Connes-Kreimer Hopf Algebra...
Tree-like Equations from the Connes-Kreimer Hopf Algebra and the Combinatorics of Chord Diagrams We describe how certain analytic Dyson-Schwinger equations and related tree-like equations arise from the universal property of the Connes-Kreimer Hopf algebra applied to Hopf subalgebras o
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
What is Abstract Algebra? (Modern Algebra)
Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in t
From playlist Abstract Algebra
Algebraic Fractions | Part 1 | Grade 7-9 Maths Series | GCSE Maths Tutor
A video revising the techniques and strategies for working with algebraic fractions. (Higher Only). This video is part of the Algebra module in GCSE maths, see my other videos below to continue with the series focussed on equations and sequences. These are the calculators that I recommen
From playlist GCSE Maths Videos
Calabi-Yau mirror symmetry: from categories to curve-counts - Tim Perutz
Tim Perutz University of Texas at Austin November 15, 2013 I will report on joint work with Nick Sheridan concerning structural aspects of mirror symmetry for Calabi-Yau manifolds. We show (i) that Kontsevich's homological mirror symmetry (HMS) conjecture is a consequence of a fragment of
From playlist Mathematics
A search for an algebraic equivalence analogue of motivic theories - Eric Friedlander
Vladimir Voevodsky Memorial Conference Topic: A search for an algebraic equivalence analogue of motivic theories Speaker: Eric Friedlander Affiliation: University of Southern California Date: September 13, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Squashing theories into Heyting algebras
This is the first of two videos on Heyting algebra, Tarski-Lindenbaum and negation: https://gist.github.com/Nikolaj-K/1478e66ccc9b7ac2ea565e743c904555 Followup video: https://youtu.be/ws6vCT7ExTY
From playlist Logic
Matt Hogancamp: Soergel bimodules and the Carlsson-Mellit algebra
The dg cocenter of the category of Soergel bimodules in type A, morally speaking, can be thought of as a categorical analogue of the ring of symmetric functions, as in joint work of myself, Eugene Gorsky, and Paul Wedrich. Meanwhile, the ring of symmetric functions is the recipient of acti
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Chris Bowman: Tautological p-Kazhdan-Lusztig Theory for cyclotomic Hecke algebras
We discuss a new explicit isomorphism between (truncations of) quiver Hecke algebras and Elias-Williamson's diagrammatic endomorphism algebras of Bott-Samelson bimodules. This allows us to deduce that the decomposition numbers of these algebras (including as examples the symmetric groups a
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
The 5 Hardest Algebraic Fractions Exam Questions | Grade 7-9 Series | GCSE Maths Tutor
A video revising the techniques and strategies for working with 5 of the hardest questions on algebraic fractions. (Higher Only). This video is part of the Algebra module in GCSE maths, see my other videos below to continue with the series focussed on equations and sequences. Revision vi
From playlist GCSE Maths Videos
What is a Module? (Abstract Algebra)
A module is a generalization of a vector space. You can think of it as a group of vectors with scalars from a ring instead of a field. In this lesson, we introduce the module, give a variety of examples, and talk about the ways in which modules and vector spaces are different from one an
From playlist Abstract Algebra