This lecture is part of an online course on rings and modules. We mainly discuss the problem of whether free modules over a ring have a well defined ran, generalizing the dimension of a vector space. We show that they do over many rings, including all non-zero commutative rings, but give
From playlist Rings and modules
Ideals in Ring Theory (Abstract Algebra)
An ideal of a ring is the similar to a normal subgroup of a group. Using an ideal, you can partition a ring into cosets, and these cosets form a new ring - a "factor ring." (Also called a "quotient ring.") After reviewing normal subgroups, we will show you *why* the definition of an ide
From playlist Abstract Algebra
RNT1.4. Ideals and Quotient Rings
Ring Theory: We define ideals in rings as an analogue of normal subgroups in group theory. We give a correspondence between (two-sided) ideals and kernels of homomorphisms using quotient rings. We also state the First Isomorphism Theorem for Rings and give examples.
From playlist Abstract Algebra
Ring Examples (Abstract Algebra)
Rings are one of the key structures in Abstract Algebra. In this video we give lots of examples of rings: infinite rings, finite rings, commutative rings, noncommutative rings and more! Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦
From playlist Abstract Algebra
Ring Oscillator Analysis Part 1
https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. Here I analyz
From playlist RF Amplifier Design
Definition of a Ring and Examples of Rings
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Ring and Examples of Rings - Definition of a Ring. - Definition of a commutative ring and a ring with identity. - Examples of Rings include: Z, Q, R, C under regular addition and multiplication The Ring of all n x
From playlist Abstract Algebra
Ring Theory: We define rings and give many examples. Items under consideration include commutativity and multiplicative inverses. Example include modular integers, square matrices, polynomial rings, quaternions, and adjoins of algebraic and transcendental numbers.
From playlist Abstract Algebra
Abstract Algebra: The definition of a Ring
Learn the definition of a ring, one of the central objects in abstract algebra. We give several examples to illustrate this concept including matrices and polynomials. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ We recommend th
From playlist Abstract Algebra
Proof: Ideal of a Ring is Proper iff it has no Units | Abstract Algebra
An ideal of a ring with identity is proper if and only if the ideal contains no units of the ring. We prove this result in today's abstract algebra video lesson! Remember that an ideal, I, of a ring, R, is an additive subgroup of I such that for all r in R and x in I, r*x and x*r are also
From playlist Abstract Algebra
Commutative algebra 4 (Invariant theory)
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. This lecture is an informal historical summary of a few results of classical invariant theory, mainly to show just how complic
From playlist Commutative algebra
The Eisenstein Ideal and its Application to W. Stein’s Conjecture....by Kenneth A. Ribet
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)
Commutative algebra 41 Locally free modules
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. We define locally free modules and explain that they are analogs of vector bundles in geometry. We give some examples of local
From playlist Commutative algebra
Commutative algebra 45: Torsion free modules
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. We finish the survey of types of modules by briefly discussing torsion-free and coprimary modules. We show that flat modules a
From playlist Commutative algebra
[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
Commutative algebra 10 (Weierstrass preparation 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 describe a second method of visualizing rings by drawing a point for each basis element of the ring. We giv
From playlist Commutative algebra
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
RNT1.2. Definition of Integral Domain
Ring Theory: We consider integral domains, which are commutative rings that contain no zero divisors. We show that this property is equivalent to a cancellation law for the ring. Finally we note some basic connections between integral domains and fields.
From playlist Abstract Algebra