Abstract algebra

Algebraic element

In mathematics, if L is a field extension of K, then an element a of L is called an algebraic element over K, or just algebraic over K, if there exists some non-zero polynomial g(x) with coefficients in K such that g(a) = 0. Elements of L which are not algebraic over K are called transcendental over K. These notions generalize the algebraic numbers and the transcendental numbers (where the field extension is C/Q, C being the field of complex numbers and Q being the field of rational numbers). (Wikipedia).

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20 The identity element

Sets might contain an element that can be identified as an identity element under some binary operation. Performing the operation between the identity element and any arbitrary element in the set must result in the arbitrary element. An example is the identity element for the binary opera

From playlist Abstract algebra

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Algebraic Expressions (Basics)

This video is about Algebraic Expressions

From playlist Algebraic Expressions and Properties

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21 The inverse element

A set might contain many inverse elements under some binary operation. To have such an element, this set must also contain an identity element under the binary operation in question. An element is an inverse element of another element in a set if performing the binary operation between t

From playlist Abstract algebra

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Ex: Write a Algebraic Expression in the Form x+c and c-x (less and more)

This video explains how to write a algebraic or variable expression from a given statement. http://mathispower4u.com

From playlist Evaluating and Writing Algebraic Expressions

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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

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Variables in Expressions and Equations

This video defines an expression and and equation. Then expressions are evaluated and the solutions to equations are considered. http://mathispower4u.com

From playlist Algebraic Structures Module

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Classify a polynomial then determining if it is a polynomial or not

šŸ‘‰ Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

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Determining if a equation is a polynomial or not

šŸ‘‰ Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

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How to evaluate an algebraic expression, x^2 + yx - (3y + x) + 2; x = -2 and y = 3

šŸ‘‰ Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)

From playlist Simplify Expressions Using Order of Operations

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Inna Entova-Aizenbud: Jacobson-Morozov Lemma for Lie superalgebras using semisimplification

I will present a generalization of the Jacobson-Morozov Lemma for quasi-reductive algebraic supergroups (respectively, Lie superalgebras), based on the idea of semisimplification of tensor categories, which will be explained during the talk. This is a joint project with V. Serganova.

From playlist Workshop: Monoidal and 2-categories in representation theory and categorification

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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

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LC001.02 - Exterior algebras

A brief introduction to exterior algebras, their universal property, the standard basis of wedge products and contraction operators. This video is a recording made in a virtual world (https://www.roblox.com/games/6461013759/metauni-Replays) of a talking board, and there may be associated

From playlist Metauni

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Representation Theory(Repn Th) 5 by Gerhard Hiss

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

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On the pioneering works of Professor I.B.S. Passi by Sugandha Maheshwari

PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund

From playlist Group Algebras, Representations And Computation

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Dimitry Gurevich - New applications of the Reflection Equation Algebras

The REA are treated to be q-analogs of the enveloping algebras U(gl(N)). In particular, each of them has a representation category similar to that of U(gl(N)). I plan to exhibit new applications of these algebras: 1. q-analog of Schur-Weyl duality 2. q-Capelli formula 3. q-Frobenius formul

From playlist Combinatorics and Arithmetic for Physics: Special Days 2022

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Geometric Algebra - Rotors and Quaternions

In this video, we will take note of the even subalgebra of G(3), see that it is isomorphic to the quaternions and, in particular, the set of rotors, themselves in the even subalgebra, correspond to the set of unit quaternions. This brings the entire subject of quaternions under the heading

From playlist Math

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Peter SCHOLZE (oct 2011) - 3/6 Perfectoid Spaces and the Weight-Monodromy Conjecture

We will introduce the notion of perfectoid spaces. The theory can be seen as a kind of rigid geometry of infinite type, and the most important feature is that the theories over (deeply ramified extensions of) Q_p and over F_p((t)) are equivalent, generalizing to the relative situation a th

From playlist Peter SCHOLZE (oct 2011) - Perfectoid Spaces and the Weight-Monodromy Conjecture

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Esteban Andruchow: Metric geometry in homogeneous spaces of the unitary group of a Cāˆ—-algebra. 1

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Analysis and its Applications

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Pere Ara: Crossed products and the Atiyah problem

Talk by Pere Are in Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/crossed-products-and-the-atiyah-problem/ on March 19, 2021.

From playlist Global Noncommutative Geometry Seminar (Americas)

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Learn how to evaluate an algebraic expression for two variables, x^2 -x+2xy-3; x= -3; y=4

šŸ‘‰ Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)

From playlist Simplify Expressions Using Order of Operations

Related pages

Field of fractions | Transcendental number | Algebraically closed field | Rational function | Vector space | Coefficient | Ideal (ring theory) | Minimal polynomial (field theory) | Algebraic number | Polynomial | Square root of 2 | Isomorphism theorems | Rational number | Polynomial ring | Homomorphism | Field extension | Mathematics | Real number | Pi | Euclidean domain | Algebraic independence | Irreducible polynomial | Complex number