In algebra, the term Hermite ring (after Charles Hermite) has been applied to three different objects. According to (p. 465), a ring is right Hermite if, for every two elements a and b of the ring, there is an element d of the ring and an invertible 2 by 2 matrix M over the ring such that (a b)M=(d 0). (The term left Hermite is defined similarly.) Matrices over such a ring can be put in Hermite normal form by right multiplication by a square invertible matrix (appendix to §I.4) calls this property K-Hermite, using Hermite instead in the sense given below. According to (§I.4, p. 26), a ring is right Hermite if any finitely generated stably free right module over the ring is free. This is equivalent to requiring that any row vector (b1,...,bn) of elements of the ring which generate it as a right module (i.e., b1R+...+bnR=R) can be completed to a (not necessarily square) invertible matrix by adding some number of rows. (The criterion of being left Hermite can be defined similarly.) (p. 528) earlier called a commutative ring with this property an H-ring. According to (§0.4), a ring is Hermite if, in addition to every stably free (left) module being free, it has IBN. All commutative rings which are Hermite in the sense of Kaplansky are also Hermite in the sense of Lam, but the converse is not necessarily true. All Bézout domains are Hermite in the sense of Kaplansky, and a commutative ring which is Hermite in the sense of Kaplansky is also a Bézout ring The Hermite ring conjecture, introduced by (p. xi), states that if R is a commutative Hermite ring, then R[x] is a Hermite ring. (Wikipedia).
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
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 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
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
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
Rings and modules 2: Group rings
This lecture is part of an online course on rings and modules. We decribe some examples of rings constructed from groups and monoids, such as group rings and rings of Dirichlet polynomials. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52XDLrm
From playlist Rings and modules
Neon Knots and Borromean Beer Rings - Numberphile
More Cliff Stoll videos: http://bit.ly/Cliff_Videos More links & stuff in full description below ↓↓↓ Our first Borromean Ring Video: https://youtu.be/x6Ml4AEt0kk Tadashi does Borromean Rings: https://youtu.be/Ra9I_-o2LHM Knot playlist: http://bit.ly/Knot-a-Phile Numberphile is supported
From playlist Cliff Stoll on Numberphile
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/PBSDSDonate Order my Maker Box from Quarterly ►► http://on.qrtr.ly/ItsOKtoMake Don’t miss the next video! SUBSCRIBE! ►► http://bit.ly/iotbs_sub ↓ More info and sources below ↓
From playlist Be Smart - LATEST EPISODES!
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
PT phase transition in non-abelian system by Haresh Raval
Non-Hermitian Physics - PHHQP XVIII DATE: 04 June 2018 to 13 June 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore Non-Hermitian Physics-"Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII" is the 18th meeting in the series that is being held over the years in Quantum Phys
From playlist Non-Hermitian Physics - PHHQP XVIII
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
Europe: The First Crusade - The People's Crusade - Extra History - #1
In 1095CE, Pope Urban gathered the leaders of the Christian community at the Council of Clermont. Urged on by Emperor Alexius Comnenos of Constantinople, he called for a crusade to retake the Holy Land from the Muslims who occupied Jerusalem. Muslims had occupied the Holy Land for over 400
From playlist Extra History (ALL EPISODES)
Philippe Michel - 3/4 Automorphic forms for GL(2)
Philippe Michel - Automorphic forms for GL(2)
From playlist École d'été 2014 - Théorie analytique des nombres
Numeric Modeling in Mathematica: Q&A with Rob Knapp
Rob Knapp answers user-submitted questions about numerical computations during Mathematica Experts Live: Numeric Modeling in Mathematica. For more information about Mathematica, please visit: http://www.wolfram.com/mathematica
From playlist Mathematica Experts Live: Numeric Modeling in Mathematica
Tropical Geometry - Lecture 3 - Fields and Varieties | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Long-term history and ephemeral configurations – Catherine Goldstein – ICM2018
Plenary Lecture 12 Long-term history and ephemeral configurations Catherine Goldstein Abstract: Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a s
From playlist Plenary Lectures
Benson Farb, Part 2: Surface bundles, mapping class groups, moduli spaces, and cohomology
29th Workshop in Geometric Topology, Oregon State University, June 29, 2012
From playlist Benson Farb: 29th Workshop in Geometric Topology
These Feisty Hermit Crabs Brawl Over Snail Shells | Deep Look
Hermit crabs are *obsessed* with snail shells. These crafty little crabs, found in California's rocky intertidal zone, are more than happy to let the snails build them a perfect home. When the crabs find a snail shell they like, they hop right into their new abode. SUBSCRIBE to Deep Look!
From playlist Deep Look | Series | KQED
Hamiltonian Simulation and Universal Quantum (...) - T. Cubitt - Main Conference - CEB T3 2017
Toby Cubitt (UCL) / 14.12.2017 Title: Hamiltonian Simulation and Universal Quantum Hamiltonians Abstract: Physical (or "analogue") Hamiltonian simulation involves engineering a Hamiltonian of interest in the laboratory, and studying its properties experimentally (somewhat analogous to b
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Buy at http://www.shapeways.com/shops/GeometricToy "Torus Magic" can eat another torus.This torus object is constructed with 30 large rings(70mm diameter) and many small rings. Copyright (c) 2015,AkiraNishihara
From playlist 3D printed toys