Sur les decompositions des algebres a division en produit tensoriel d'algebres cycliques Pages Tignol, J. Local structure of maximal orders on surfaces Pages Artin, M. Left ideals in maximal orders Pages Artin, M. Brauer-Severi varieties Pages Artin, M.

## Ring theory

The Brauer groups in complex geometry Pages Elencwajg, G. Pages Hoobler, Raymond T. The Brauer group of a quasi affine-scheme Pages Verschoren, Alain. A check list on Brauer groups Pages Verschoren, A. Show next xx. My main research is in approximation theory, Fourier analysis, orthogonal polynomials and special functions, which are really all connected. Most of my work focuses on multidimensional problems. I work in enumerative, bijective and algebraic combinatorics.

Most of what I am working on at the moment is related to the dimer model, or to Schubert calculus and the combinatorics of reduced words. I use computers heavily in my work.

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University of Oregon. UO Home Dept Index. Faculty Research Interests Nicolas Addington : algebraic geometry I work in algebraic geometry, mainly using derived categories of coherent sheaves.

Yashar Ahmadian : theoretical neuroscience, statistical physics, random matrix theory My research is in the field of theoretical neuroscience. Arkady Berenstein : quantum groups, representation theory, algebraic combinatorics My research interests include Representation Theory of Lie algebras, Quantum Groups, and Coxeter Groups, Hopf Algebras, Algebraic Combinatorics Cluster algebras, Noncommutative Algebra and related aspects.

Group representations Coxeter groups Lie algebra representations Hopf algebras Quantum Group Cluster algebra Noncommutative algebraic geometry Boris Botvinnik : differential topology, positive scalar curvature, Morse theory I study algebraic topology and differential geometry, with a focus on conformal geometry and the space of metrics of positive scalar curvature.

Marcin Bownik : harmonic analysis, wavelets, approximation theory I work in the area of harmonic analysis and wavelets. Dan Dugger : homotopy theory, K-theory, homological algebra Most of my work is in motivic and equivariant homotopy theory, these days largely focused on the latter. Ellen Eischen : number theory I work primarily in number theory, especially algebraic number theory.

Ben Elias : representation theory, categorification I study categorical representation theory, a relatively new field that takes representation theory to the next level. Peter Gilkey : higher-signature differential geometry, heat trace analysis I work in pseudo-Riemannian geometry. Weiyong He : differential geometry and partial differential equations Complex geometry and Kahler geometry, extremal metrics and Calabi flow.

## Algebraic Geometry

Geometric evolution equations, mean curvature flow. Nonlinear partial differential equations. Alexander Kleshchev : representation theory, Lie theory, group theory I study representation theory of Lie algebras, algebraic groups and related objects, such as symmetric groups, Hecke algebras, etc. David Levin : Markov chains and random walks, multiparameter processes, potential theory My research is in probability theory, including: random walks, Markov chains, multiparameter processes, jump processes, and related potential theory.

Robert Lipshitz : low-dimensional and symplectic topology I use techniques from symplectic geometry and, to a lesser extent, algebraic topology and abstract algebra, to study questions about knots and 3- and 4-dimensional manifolds.

Peng Lu : geometric analysis, Ricci flow, complex geoemtry My research is in geometric analysis. Luca Mazzucato : theoretical neuroscience My current research interests are in theoretical neuroscience. Victor Ostrik : geometric Lie theory, tensor categories, Hopf algebras I am currently interested in the categorification of ring theory, that is study of tensor categories and module categories over them, and in geometric representation theory, which means study of representation theoretic questions using tools from algebraic geometry perverse sheaves and D-modules.

Peter Ralph : mathematical biology, evolution, statistics I work on probability and statistics as applied to understanding ecology and evolution, in particular developing new stochastic models of biological evolution and using statistical inference and visualization methods to find out what genomes can tell us about biology. Yefeng Shen : algebraic geometry and mathematical physics I am interested in algebraic geometry and mathematical physics.

Chris Sinclair : random matrix theory, heights of polynomials I am interested in the statistics of eigenvalues of random matrices and the roots of random polynomials. Dev Sinha : rational homotopy theory, knot theory, operads I work in a range of topics in topology, mostly in algebraic topology but some in geometric topology as well. Arkady Vaintrob : algebraic geometry, knot theory, mathematical physics, Lie theory I study algebra and geometry motivated by physics.

Milne: A Primer of Commutative Algebra. Read more. Home Questions Tags Users Unanswered. Introduction to ring theory? Ask Question. Asked 5 years, 10 months ago.

Active 2 years, 7 months ago. Viewed 2k times. I started to read about rings and got really excited. Martin Sleziak 52k 13 13 gold badges silver badges bronze badges. If you'd like to learn commutative algebra and it sounds like you would! Popular texts are Herstein and Artin for an introductory book, and Hungerford and Lang I love Hungerford once you've gone through one of the former.

## Ring Theory And Algebraic Geometry - CRC Press Book

Georges Elencwajg Georges Elencwajg k 8 8 gold badges silver badges bronze badges. I think the authors assume some familarity with the notion of rings, or at least assume some mathematical maturity. The reason is that the proofs are quite short though, complete and many stuff is covered by the exercises, which other books would include into the text. That being said, I think you can become a good mathematician when you try to solve all the exercises in this book. Yes, you are right: although technically the authors assume only few previous results, the book definitely presupposes a certain maturity of its readers.

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So indeed they would read the book with more profit if they were already comfortable with the main notions in a first course in general abstract algebra, as developed in Mike Artin's Algebra for example although reading that book in its entirety is certainly not required.

Working your own way through it without any ring theory background would be valuable to someone highly talented, and inefficient for almost anyone else. Dori Bejleri Dori Bejleri 4, 1 1 gold badge 12 12 silver badges 20 20 bronze badges. Rodney Coleman Rodney Coleman 3 3 silver badges 6 6 bronze badges. Alfred Yerger Alfred Yerger Aims Aims 1 1 1 bronze badge. Sign up or log in Sign up using Google.