Advanced Modern Algebra by Joseph J Rotman
This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different organization than the first. It begins with a discussion of the cubic and quartic equations, which leads into permutations, group theory, and Galois theory (for finite extensions; infinite Galois theory is discussed later in the book). The study of groups continues with finite abelian groups (finitely generated groups are discussed later, in the context of module theory), Sylow theorems, simplicity of projective unimodular groups, free groups and presentations, and the Nielsen-Schreier theorem (subgroups of free groups are free). The study of commutative rings continues with prime and maximal ideals, unique factorization, noetherian rings, Zorn's lemma and applications, varieties, and Grobner bases. Next, noncommutative rings and modules are discussed, treating tensor product, projective, injective, and flat modules, categories, functors, and natural transformations, categorical constructions (including direct and inverse limits), and adjoint functors. Then follow group representations: Wedderburn-Artin theorems, character theory, theorems of Burnside and Frobenius, division rings, Brauer groups, and abelian categories. Advanced linear algebra treats canonical forms for matrices and the structure of modules over PIDs, followed by multilinear algebra. Homology is introduced, first for simplicial complexes, then as derived functors, with applications to Ext, Tor, and cohomology of groups, crossed products, and an introduction to algebraic $K$-theory. Finally, the author treats localization, Dedekind rings and algebraic number theory, and homological dimensions. The book ends with the proof that regular local rings have unique factorization. (GSM/114)-
Analysis
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Options Pricing and Portfolio Optimization
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Scrapbook of Complex Curve Theory
- Partial Differential Equations
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Algebra
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A Course on the Web Graph
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Global Analysis
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Invitation to Nonlinear Algebra
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Applied Asymptotic Analysis
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A Course in Operator Theory
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Representations of Finite and Compact Groups
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Classical and Quantum Computation
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Toric Varieties
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Introduction to Analytic and Probabilistic Number Theory
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Mathematical Methods in Quantum Mechanics
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Discovering Modern Set Theory, Part 1
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Differential Geometry, Lie Groups, and Symmetric Spaces
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Lectures on Elliptic and Parabolic Equations in Sobolev Spaces
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Riemann Surfaces by Way of Complex Analytic Geometry
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Advanced Modern Algebra, Parts 1 and 2
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Introduction to Quantum Groups and Crystal Bases
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Introduction to the H-Principle
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A Course in Differential Geometry
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Measure Theory and Integration
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Algebraic Number Fields
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Inequalities in Matrix Algebras
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Algebraic Curves and Riemann Surfaces
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$\textrm {C}^*$-Algebras and Finite-Dimensional Approximations
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The Calderon Problem
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Mathematical Foundations of Deep Learning Models and Algorithms
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Several Complex Variables with Connections to Algebraic Geometry and Lie Groups
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Function Theory of One Complex Variable
| SKU | Unavailable |
| ISBN 13 | 9780821847411 |
| ISBN 10 | 0821847414 |
| Title | Advanced Modern Algebra |
| Author | Joseph J Rotman |
| Series | Graduate Studies In Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | American Mathematical Society |
| Year published | 2010-08-30 |
| Number of pages | 1008 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |