Introduction to modern algebra and its applications
Elements of number theory -- Elements of group theory -- Examples of groups -- Elements of ring theory -- Polynomial rings in one variable -- Elements of field theory -- Examples of applications -- Polynomials in several variables -- Finite fields and their applications -- Finite dimensional algebra...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Boca Raton, FL, London, New York
CRC Press, Taylor & Francis Group
2021
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| Schriftenreihe: | A science publishers book
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| Schlagworte: | |
| Online Zugang: | zbMATH |
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Tag hinzufügen | Zusammenfassung: | Elements of number theory -- Elements of group theory -- Examples of groups -- Elements of ring theory -- Polynomial rings in one variable -- Elements of field theory -- Examples of applications -- Polynomials in several variables -- Finite fields and their applications -- Finite dimensional algebras -- Applications of quaternions and octonions. "The book provides an introduction to modern abstract algebra and its applications. It covers all major topics of classical theory of numbers, groups, rings, fields and finite dimensional algebras. The book also provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. In particular, it considers algorithm RSA, secret sharing algorithms, Diffie-Hellman Scheme and ElGamal cryptosystem based on discrete logarithm problem. It also presents Buchberger's algorithm which is one of the important algorithms for constructing Gröbner basis. The Cayley-Dickson construction for finite dimensional algebras is described. The structure and properties of quaternions and octonions are studied in details and their applications in the number theory and computer graphics are presented"-- |
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| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | ix, 384 Seiten Illustrationen |
| ISBN: | 9780367820916 978-0-367-82091-6 |