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1. |
Record Nr. |
UNINA9910462709003321 |
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Autore |
Stahl Saul |
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Titolo |
Introductory modern algebra : a historical approach / / Saul Stahl |
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Pubbl/distr/stampa |
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Hoboken, New Jersey : , : Wiley, , 2013 |
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©2013 |
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ISBN |
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1-118-83752-5 |
1-118-55203-2 |
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Edizione |
[Second edition.] |
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Descrizione fisica |
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1 online resource (691 p.) |
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Disciplina |
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Soggetti |
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Algebra, Abstract |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Cover; Half Title page; Title page; Copyright page; Preface; Chapter 1: The Early History; 1.1 The Breakthrough; Chapter 2: Complex Numbers; 2.1 Rational Functions of Complex Numbers; 2.2 Complex Roots; 2.3 Solvability by Radicals I; 2.4 Ruler-and-Compass Constructibility of Regular Polygons; 2.5 Orders of Roots of Unity; 2.6 The Existence of Complex Numbers; Chapter 3: Solutions of Equations; 3.1 The Cubic Formula; 3.2 Solvability by Radicals II; 3.3 Other Types of Solutions; Chapter 4: Modular Arithmetic; 4.1 Modular Addition, Subtraction, and Multiplication |
4.2 The Euclidean Algorithm and Modular Inverses4.3 Radicals in Modular Arithmetic; 4.4 The Fundamental Theorem of Arithmetic; Chapter 5: The Binomial Theorem and Modular Powers; 5.1 The Binomial Theorem; 5.2 Fermat's Theorem and Modular Exponents; 5.3 The Multinomial Theorem; 5.4 The Euler φ-Function; Chapter 6: Polynomials Over A Field; 6.1 Fields and Their Polynomials; 6.2 The Factorization of Polynomials; 6.3 The Euclidean Algorithm for Polynomials; 6.4 Elementary Symmetric Polynomials; 6.5 Lagrange's Solution of the Quartic Equation; Chapter 7: Galois Fields |
7.1 Galois's Construction of His Fields7.2 The Galois Polynomial; 7.3 The Primitive Element Theorem; 7.4 On the Variety of Galois Fields; Chapter 8: Permutations; 8.1 Permuting the Variables of a Function I; |
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8.2 Permutations; 8.3 Permuting the Variables of a Function II; 8.4 The Parity of a Permutation; Chapter 9: Groups; 9.1 Permutation Groups; 9.2 Abstract Groups; 9.3 Isomorphisms of Groups and Orders of Elements; 9.4 Subgroups and Their Orders; 9.5 Cyclic Groups and Subgroups; 9.6 Cayley's Theorem; Chapter 10: Quotient Groups and Their Uses; 10.1 Quotient Groups; 10.2 Group Homomorphisms |
10.3 The Rigorous Construction of Fields10.4 Galois Groups and the Resolvability of Equations; Chapter 11: Topics in Elementary Group Theory; 11.1 The Direct Product of Groups; 11.2 More Classifications; Chapter 12: Number Theory; 12.1 Pythagorean Triples; 12.2 Sums of Two Squares; 12.3 Quadratic Reciprocity; 12.4 The Gaussian Integers; 12.5 Eulerian Integers and Others; 12.6 What Is the Essence of Primality?; Chapter 13: The Arithmetic of Ideals; 13.1 Preliminaries; 13.2 Integers of a Quadratic Field; 13.3 Ideals; 13.4 Cancelation of Ideals; 13.5 Norms of Ideals |
13.6 Prime Ideals and Unique Factorization13.7 Constructing Prime Ideals; Chapter 14: Abstract Rings; 14.1 Rings; 14.2 Ideals; 14.3 Domains; 14.4 Quotients of Rings; A. Excerpts from Al-Khwarizmi's Solution of the Quadratic Equation1; B. Excerpts from Cardano's Ars Magna1; C. Excerpts from Abel's A Demonstration of the Impossibility of the Algebraic Resolution of General Equations Whose Degree Exceeds Four1; D. Excerpts from Galois's On the Theory of Numbers1; E. Excerpts from Cayley's The Theory of Groups1; F. Mathematical Induction; G. Logic, Predicates, Sets, and Functions |
G.1 Truth Tables |
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Sommario/riassunto |
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Praise for the First Edition ""Stahl offers the solvability of equations from the historical point of view...one of the best books available to support a one-semester introduction to abstract algebra.""-CHOICE Introductory Modern Algebra: A Historical Approach, Second Edition presents the evolution of algebra and provides readers with the opportunity to view modern algebra as a consistent movement from concrete problems to abstract principles. With a few pertinent excerpts from the writings of some of the greatest mathematicians, the Second Edition |
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2. |
Record Nr. |
UNINA9910463767503321 |
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Autore |
Köffer Timo |
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Titolo |
Basel III, Implications for banks' capital structure : what happens with hybrid capital instruments? / / Timo Köffer |
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Pubbl/distr/stampa |
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Hamburg, Germany : , : Anchor Academic Publishing, , 2014 |
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©2014 |
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ISBN |
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Descrizione fisica |
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1 online resource (67 p.) |
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Disciplina |
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Soggetti |
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Corporate governance - Law and legislation - Great Britain |
Corporation law - Great Britain |
Corporations - Finance |
Convertible securities - Law and legislation |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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Basel III - Implications for banks` capital structure; Content; List of abbreviations; List of figures and tables; 1. Introduction; 2. Basel III; 2.1 History; 2.2 Implementation and objectives of Basel III; 2.3 Comparison of the capital definition of Basel II and Basel III; 2.4 Critical consideration of Basel III; 3. Hybrid capital; 3.1 The market for hybrid capital; 3.2 Silent partnership; 3.3 Participatory notes; 3.4 Subordinated liabilities; 3.5 Trust preferred securities; 3.6 Convertible- and warrant bonds; 4. Contingent capital; 4.1 Contingent convertible bonds |
4.2 Contingent convertible bonds examples 4.3 Critical assessment of the suitability as a component of core capital; 4.4 The market for contingent convertible bonds; 4.5 The features of contingent convertible bonds; 5. Impact of Basel III; 5.1 Impact on banks funding structure; 5.2 Impact on banks hybrid capital; 5.3. Impact on Commerzbank AG; 6. Conclusion; Bibliography |
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Sommario/riassunto |
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This book attempts to answer the question of how CoCos differ from convertible bonds, and how these instruments are suitable for contributing as core capital under Basel III. The place ability of CoCos and the challenges resulting from their use are discussed in this book. |
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Overall a comprehensive picture of the impacts resulting from the new capital definitions will be created. The Background to the introduction of Basel III is described at the beginning of the book, in addition to a presentation of the Basel III document and the new capital definitions. To create a kind of basic understandin |
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