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
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
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define coherent modules over rings and coherent sheaves, and then discuss when the amps f* and f_* preserve coherence or quasicoherence.
From playlist Algebraic geometry II: Schemes
Ring Definition (expanded) - Abstract Algebra
A ring is a commutative group under addition that has a second operation: multiplication. These generalize a wide variety of mathematical objects like the integers, polynomials, matrices, modular arithmetic, and more. In this video we will take an in depth look at the definition of a rin
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
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
Units in a Ring (Abstract Algebra)
The units in a ring are those elements which have an inverse under multiplication. They form a group, and this “group of units” is very important in algebraic number theory. Using units you can also define the idea of an “associate” which lets you generalize the fundamental theorem of ar
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
Visual Group Theory, Lecture 7.1: Basic ring theory
Visual Group Theory, Lecture 7.1: Basic ring theory A ring is an abelian group (R,+) with a second binary operation, multiplication and the distributive law. Multiplication need not commute, nor need there be multiplicative inverses, so a ring is like a field but without these properties.
From playlist Visual Group Theory
James Borger: The geometric approach to cohomology Part I
SMRI Seminar Course: 'The geometric approach to cohomology' Part I James Borger (Australian National University) Abstract: The aim of these two talks is to give an overview of the geometric aka stacky approach to various cohomology theories for schemes: de Rham, Hodge, crystalline and pr
From playlist SMRI Course: The geometric approach to cohomology
Schemes 27: Quasicoherent sheaves
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We show how to turn a module over a ring into a sheaf of modules over its spectrum. A quasicoherent sheaf of modules of one which looks locally like one constr
From playlist Algebraic geometry II: Schemes
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. Given a morphism of schemes, we define two maps f^* and f_* taking sheaves of modules on one space to sheaves of modules on the other, and discuss their exac
From playlist Algebraic geometry II: Schemes
Operational K-theory - Sam Payne
Sam Payne March 13, 2015 Workshop on Chow groups, motives and derived categories More videos on http://video.ias.edu
From playlist Mathematics
Duality in Algebraic Geometry by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
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
Coherent (phi, Gamma)-modules and cohomology of local systems 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) Eknat
From playlist Perfectoid Spaces 2019