In algebra, an augmentation of an associative algebra A over a commutative ring k is a k-algebra homomorphism , typically denoted by ε. An algebra together with an augmentation is called an augmented algebra. The kernel of the augmentation is a two-sided ideal called the augmentation ideal of A. For example, if is the group algebra of a finite group G, then is an augmentation. If A is a graded algebra which is connected, i.e. , then the homomorphism which maps an element to its homogeneous component of degree 0 is an augmentation. For example, is an augmentation on the polynomial ring . (Wikipedia).
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
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
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
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
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
Abstract Algebra | Injective Functions
We give the definition of an injective function, an outline of proving that a given function is injective, and a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
16 You have made it to the first exciting video Operations
To be honest, the topics have been very dry up to now. Here is the first bit of excitement. Operations. Understanding operations is a fundamental priority in abstract algebra.
From playlist Abstract algebra
How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y
From playlist Introducing linear algebra
Intermediate Algebra-Exponential Functions and Equations
Intermediate Algebra-Exponential Functions and Equations
From playlist Intermediate Algebra
Hierarchies of contact manifolds via rational SFT - Zhengyi Zhou
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Hierarchies of contact manifolds via rational SFT Speaker: Zhengyi Zhou Affiliation: Member, School of Mathematics Date: December 11, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
The Zassenhaus Conjecture for cyclic-by-abelian groups by Angel del Rio
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
Augmentations, generating families and micro local sheaves by Michael G Sullivan
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
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
Friedrich Wagemann: Deformation quantization of Leibniz algebras
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 Algebra
Toward a contact Fukaya category - Lenny Ng
Toward a contact Fukaya category Augmentations and Legendrians at the IAS Topic: Toward a contact Fukaya category Speaker: Lenny Ng Date: Thursday, February 11 I will describe some work in progress (maybe more accurately, wild speculation) regarding a version of the derived Fukaya categor
From playlist Mathematics
Support Varieties for Modular Representations - Eric M. Friedlander
Members’ Seminar Topic: Support Varieties for Modular Representations Speaker: Eric M. Friedlander Affiliation: University of Southern California; Member, School of Mathematics Date: November 30, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Free Group Rings by I. B. S. Passi
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
Torsion units of integral group rings (Lecture 1) by Angel del Rio
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
Quantitative Legendrian geometry - Michael Sullivan
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Quantitative Legendrian geometry Speaker: Michael Sullivan Affiliation: University of Massachusetts, Amherst Date: January 14, 2022 I will discuss some quantitative aspects for Legendrians in a (more or less
From playlist Mathematics
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