FIT2.3.3. Algebraic Extensions
Field Theory: We define an algebraic extension of a field F and show that successive algebraic extensions are also algebraic. This gives a useful criterion for checking algberaic elements. We finish with algebraic closures.
From playlist Abstract Algebra
Algebraic and Transcendental Elements; Finite Extensions - Field Theory - Lecture 01
In this video we introduce the notion of algebraic and transcendental. We then introduce a notion of "finite extension" which will help us prove every element in an extension is algebraic. See @MatthewSalomone's Abstract Algebra 2 videos. They complement this presentation with better exa
From playlist Field Theory
Algebraic Expressions (Basics)
This video is about Algebraic Expressions
From playlist Algebraic Expressions and Properties
Field Definition (expanded) - Abstract Algebra
The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They
From playlist Abstract Algebra
Field Theory: We consider the case of simple extensions, where we adjoin a single element to a given field. The cases of transcendental and algebraic arise, depending on whether the kernel of the evaluation map is zero or not. In the algebraic case, we define the minimal polynomial, show
From playlist Abstract Algebra
Extending arithmetic to infinity! | Real numbers and limits Math Foundations 103 | N J Wildberger
We are interested in investigating how to rigorously and carefully extend arithmetic with rational numbers to a wider domain involving the symbol 1/0, represented by a ``sideways 8''. First we have a look at the simpler case of natural number arithmetic, where extending to infinity is re
From playlist Math Foundations
Evaluating Algebraic Expressions
In this video we discuss the basic principles for evaluating algebraic expressions, including order of operations and the importance of parentheses.
From playlist College Algebra
The integers modulo n under addition is a group. What are the integers mod n, though? In this video I take you step-by-step through the development of the integers mod 4 as an example. It is really easy to do and to understand.
From playlist Abstract algebra
Galois theory: Field extensions
This lecture is part of an online course on Galois theory. We review some basic results about field extensions and algebraic numbers. We define the degree of a field extension and show that a number is algebraic over a field if and only if it is contained in a finite extension. We use thi
From playlist Galois theory
23 Algebraic system isomorphism
Isomorphic algebraic systems are systems in which there is a mapping from one to the other that is a one-to-one correspondence, with all relations and operations preserved in the correspondence.
From playlist Abstract algebra
Galois theory: Transcendental extensions
This lecture is part of an online graduate course on Galois theory. We describe transcendental extension of fields and transcendence bases. As applications we classify algebraically closed fields and show hw to define the dimension of an algebraic variety.
From playlist Galois theory
Christopher Schafhauser: On the classification of nuclear simple C*-algebras, Lecture 4
Mini course of the conference YMC*A, August 2021, University of Münster. Abstract: A conjecture of George Elliott dating back to the early 1990’s asks if separable, simple, nuclear C*-algebras are determined up to isomorphism by their K-theoretic and tracial data. Restricting to purely i
From playlist YMC*A 2021
Title: Strongly Étale Difference Algebras and Babbitt's Decomposition
From playlist Fall 2015
On the notion of genus for division algebras and algebraic groups - Andrei Rapinchu
Joint IAS/Princeton University Number Theory Seminar Topic: On the notion of genus for division algebras and algebraic groups Speaker: Andrei Rapinchu Affiliation: University of Virginia Date: November 2, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Francesca Arici: SU(2)-symmetries and exact sequences of C*-algebras through subproduct systems
Talk by Francesca Arici in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on November 17, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Perfectoid spaces (Lecture 1) by Kiran Kedlaya
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
Field Theory - Sums and Products of Algebraics are Algebraic -Lecture 6
In this video we prove that sums and products of algebraic elements are algebraic.
From playlist Field Theory
