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
Commutative algebra 11 (Spectrum of a ring)
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 define the spectrum of a ring as the space of prime ideals, and give a few examples. Reading: Lectures 9
From playlist Commutative 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 Network - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
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
Rings and midules 3: Burnside ring and rings of differential operators
This lecture is part of an online course on rings and modules. We discuss a few assorted examples of rings. The Burnside ring of a group is a ring constructed form the permutation representations. The ring of differentail operators is a ring whose modules are related to differential equat
From playlist Rings and modules
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 Theory: We define ring homomorphisms, ring isomorphisms, and kernels. These will be used to draw an analogue to the connections in group theory between group homomorphisms, normal subgroups, and quotient groups.
From playlist Abstract Algebra
Commutative algebra 13 (Topology of Spec R)
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 discuss the topology of the spectrum Spec R of a ring, showing that it is compact, sometimes connected, an
From playlist Commutative algebra
Commutative algebra 12: Examples of Spec R
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 give some examples of the spectrum of a ring, including the rings of Gaussian integers, polynomials and power series in 2 v
From playlist Commutative algebra
Schemes 5: Definition of a scheme
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We give some historical background, then give the definition of a scheme and some simple examples, and finish by explaining the origin of the word "spectrum".
From playlist Algebraic geometry II: Schemes
Schemes 23: Valuations and separation
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.. We state a condition for morphisms of schemes to be separated in therms of discrete valuation rings, and apply this to the line with two origins and the proje
From playlist Algebraic geometry II: Schemes
Benjamin Böhme: The Dress splitting and equivariant commutative multiplications
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: Workshop "Fusion systems and equivariant algebraic topology"
From playlist HIM Lectures: Junior Trimester Program "Topology"
Commutative algebra 18 (Functions on Spec R)
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 explain how to consider elements of a ring R as functions on the space Spec R, taking values at each point
From playlist Commutative algebra
Haldun Özgür Bayindir : Adjoining roots to ring spectra and algebraic 𝐾-theory
CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 24, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR
From playlist Topology
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We give two examples of gluing affine schemes to get non-affine schemes: the line with two origins and the projective line. We calculate the regular functions
From playlist Algebraic geometry II: Schemes
Schemes 7: More examples of Spec R
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We discuss several more examples of the spectrum of rings, and compare the spectrum of a curve with the spectrum of a number field.
From playlist Algebraic geometry II: Schemes
Abstract Algebra 2.1: Introduction to Rings
In this video, I will introduce rings and basic examples of rings. Translate This Video : http://www.youtube.com/timedtext_video?ref=share&v=jesyk7_ti6Q Notes : None yet Patreon : https://www.patreon.com/user?u=16481182 Teespring : https://teespring.com/stores/fematika Email : fematikaqna
From playlist Abstract Algebra
Commutative algebra 15 (Noetherian spaces)
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 define Noetherian topological spaces, and use them to show that for a Noetherian ring R, every closed subse
From playlist Commutative algebra