Ordered groups | Real algebraic geometry
In abstract algebra, an ordered ring is a (usually commutative) ring R with a total order ≤ such that for all a, b, and c in R: * if a ≤ b then a + c ≤ b + c. * if 0 ≤ a and 0 ≤ b then 0 ≤ ab. (Wikipedia).
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
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
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
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
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
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
How It's Made: Class and Championship Rings
Stream Full Episodes of How It's Made: https://www.discoveryplus.com/show/how-its-made Subscribe to Science Channel: http://bit.ly/SubscribeScience Like us on Facebook: https://www.facebook.com/ScienceChannel Follow us on Twitter: https://twitter.com/ScienceChannel Follow us on Instag
From playlist How It's Made
Abstract Algebra | Types of rings.
We define several and give examples of different types of rings which have additional structure. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Kirsten Eisenträger: Computing endomorphism rings of supersingular elliptic curves
CIRM HYBRID EVENT Computing endomorphism rings of supersingular elliptic curves is an important problem in computational number theory, and it is also closely connected to the security of some of the recently proposed isogeny-based cryptosystems. In this talk we give a new algorithm for co
From playlist Number Theory
Nonlinear algebra, Lecture 1: "Polynomials, Ideals, and Groebner Bases", by Bernd Sturmfels
This is the first lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences. Topics covered: polynomilas, ideals and Groebner bases.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Rings 6 Prime and maximal ideals
This lecture is part of an online course on rings and modules. We discuss prime and maximal ideals of a (commutative) ring, use them to construct the spectrum of a ring, and give a few examples. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj5
From playlist Rings and modules
"New Paradigms in Invariant Theory" - Roger Howe, Yale University [2011]
HKUST Institute for Advanced Study Distinguished Lecture New Paradigms in Invariant Theory Speaker: Prof Roger Howe, Yale University Date: 13/6/2011 Video taken from: http://video.ust.hk/Watch.aspx?Video=6A41D5F6B1A790DC
From playlist Mathematics
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.. We review valuation rings. We give a few examples of discrete and non-discrete valuation rings, and give a brief sketch of how non-discrete valuation rings us
From playlist Algebraic geometry II: Schemes
Structure of group rings and the group of units of integral group rings (Lecture 1) by Eric Jespers
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 fun
From playlist Group Algebras, Representations And Computation
The Structure of the Group of Rational Points of an Abelian Variety (CTNT Online, June 12-14, 2020)
This video was created for the CTNT 2020 Conference (June 12-14, 2020): https://ctnt-summer.math.uconn.edu/ctnt-conference-2020-online/ (Preprint) The Structure of the Group of Rational Points of an Abelian Variety over a Finite Field: https://arxiv.org/abs/2006.00637 My contact informat
From playlist CTNT 2020 - Conference Videos
The Simplifying Synthesis Ultimate Guide To Rules for Ring Closure
An organic chemistry lesson on Baldwins Rules and Beckwith Rules for ring closing reactions. SUPPORT THE CHANNEL ON PATREON: https://www.patreon.com/SimplifyingSy... Socials: https://www.instagram.com/simplifying... https://twitter.com/SimplifyingSyn1 https://www.facebook.com/Simplifyi
From playlist Ultimate Guides
Alexandra SHLAPENTOKH - Defining Valuation Rings and Other Definability Problems in Number Theory
We discuss questions concerning first-order and existential definability over number fields and function fields in the language of rings and its extensions. In particular, we consider the problem of defining valuations rings over finite and infinite algebraic extensions
From playlist Mathematics is a long conversation: a celebration of Barry Mazur
By Differential Algebra we mean rings with extra operations. In this video we show how to encode rings with extra operations using birings/affine ring schemes. This video was hacked together. Let me know if you have no idea what I'm talking about. I plan to use this later.
From playlist Birings
Schemes 46: Differential operators
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we define differential operators on rings, and calculate the universal (normalized) differential operator of order n. As a special case we fin
From playlist Algebraic geometry II: Schemes