Problems in abstract algebra / A. R. Wadsworth

By:

Wadsworth, Adrian R, 1947- [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: American Mathematical Society. Student mathematical library ; volume 82Publisher: Providence, Rhode Island : American Mathematical Society, [2017]Distributor: [Ipswich, Massachusetts] : EBSCO IndustriesDescription: 1 Online-Ressource (viii, 277 Seiten) : Illustrationen ; 21,5 cmISBN:

9781470440442

Subject(s):

Additional physical formats: 9781470435837 | 147044044X | 1470435837 | 9781470440442 | Erscheint auch als: Problems in abstract algebra. Druck-Ausgabe Providence, Rhode Island : AMS, American Mathematical Society, 2017. viii, 277 Seiten | Print version: Problems in Abstract Algebra. Providence : American Mathematical Society,c2017MSC: MSC: 12-01 | *12-01 | 13-01 | 15-01 | 20-01 | 00A07RVK: RVK: SK 200LOC classification:

QA162

Online resources:

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Summary: This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups)Summary: 3.3. Polynomial rings and evaluation maps3.4. Integral domains, quotient fields; 3.5. Maximal ideals and prime ideals; 3.6. Divisibility and principal ideal domains; 3.7. Unique factorization domains; Chapter 4. Linear Algebra and Canonical Forms of Linear Transformations; 4.1. Vector spaces and linear dependence; 4.2. Linear transformations and matrices; 4.3. Dual space; 4.4. Determinants; 4.5. Eigenvalues and eigenvectors, triangulation and diagonalization; 4.6. Minimal polynomials of a linear transformation and primary decomposition; 4.7. -cyclic subspaces and -annihilatorsSummary: 4.8. Projection maps4.9. Cyclic decomposition and rational and Jordan canonical forms; 4.10. The exponential of a matrix; 4.11. Symmetric and orthogonal matrices over \R; 4.12. Group theory problems using linear algebra; Chapter 5. Fields and Galois Theory; 5.1. Algebraic elements and algebraic field extensions; 5.2. Constructibility by compass and straightedge; 5.3. Transcendental extensions; 5.4. Criteria for irreducibility of polynomials; 5.5. Splitting fields, normal field extensions, and Galois groups; 5.6. Separability and repeated roots; 5.7. Finite fields; 5.8. Galois field extensionsSummary: 5.9. Cyclotomic polynomials and cyclotomic extensions5.10. Radical extensions, norms, and traces; 5.11. Solvability by radicals; Suggestions for Further Reading; Bibliography; Index of Notation; Subject and Terminology Index; Back CoverSummary: Cover; Title page; Contents; Preface; Introduction; 0.1. Notation; 0.2. Zorn's Lemma; Chapter 1. Integers and Integers mod ; Chapter 2. Groups; 2.1. Groups, subgroups, and cosets; 2.2. Group homomorphisms and factor groups; 2.3. Group actions; 2.4. Symmetric and alternating groups; 2.5. -groups; 2.6. Sylow subgroups; 2.7. Semidirect products of groups; 2.8. Free groups and groups by generators and relations; 2.9. Nilpotent, solvable, and simple groups; 2.10. Finite abelian groups; Chapter 3. Rings; 3.1. Rings, subrings, and ideals; 3.2. Factor rings and ring homomorphismsPPN: PPN: 897974387Package identifier: Produktsigel: ZDB-4-NLEBK

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