Nadiya Gubareni's Books

Algebras, Rings and Modules

Volume 1

By: Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko

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Algebras, Rings and Modules

Volume 1

By: Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko

Accosiative rings and algebras are very interesting algebraic structures. In a strict sense, the theory of algebras (in particular, noncommutative algebras) originated fromasingleexample,namelythequaternions,createdbySirWilliamR.Hamilton in1843. Thiswasthe?rstexampleofanoncommutative”numbersystem”. During thenextfortyyearsmathematiciansintroducedotherexamplesofnoncommutative algebras, began to bring some order into them and to single out certain types of algebras for special attention. Thus, low-dimensional algebras, division algebras, and commutative algebras, were classi?ed and characterized. The ?rst complete results in the structure theory of associative algebras over the real and complex ?elds were obtained by T.Molien, E.Cartan and G.Frobenius. Modern ring theory began when J.H.Wedderburn proved his celebrated cl- si?cation theorem for ?nite dimensional semisimple algebras over arbitrary ?elds. Twenty years later, E.Artin proved a structure theorem for rings satisfying both the ascending and descending chain condition which generalized Wedderburn structure theorem. The Wedderburn-Artin theorem has since become a corn- stone of noncommutative ring theory. The purpose of this book is to introduce the subject of the structure theory of associative rings. This book is addressed to a reader who wishes to learn this topic from the beginning to research level. We have tried to write a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and related structures and will be accessible for independent study.

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Page Count

393

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402026919

ISBN 13

9781402026911

Introduction to Modern Algebra and Its Applications

By: Nadiya Gubareni

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Introduction to Modern Algebra and Its Applications

By: Nadiya Gubareni

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. Key Features: Covers all major topics of classical theory of modern abstract algebra such as groups, rings and fields and their applications. In addition it provides the introduction to the number theory, theory of finite fields, finite dimensional algebras and their applications. Provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. Presents numerous examples illustrating the theory and applications. It is also filled with a number of exercises of various difficulty. Describes in detail the construction of the Cayley-Dickson construction for finite dimensional algebras, in particular, algebras of quaternions and octonions and gives their applications in the number theory and computer graphics.

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395

Publisher

CRC Press

Published Date

ISBN 10

1000209474

ISBN 13

9781000209471

Algebras, Rings and Modules, Volume 2

Non-commutative Algebras and Rings

By: Michiel Hazewinkel,Nadiya M. Gubareni

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Algebras, Rings and Modules, Volume 2

Non-commutative Algebras and Rings

By: Michiel Hazewinkel,Nadiya M. Gubareni

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.

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Page Count

364

Publisher

CRC Press

Published Date

ISBN 10

1351869876

ISBN 13

9781351869874

Book's by Nadiya Gubareni

Algebras, Rings and Modules

Algebras, Rings and Modules

Introduction to Modern Algebra and Its Applications

Introduction to Modern Algebra and Its Applications

Algebras, Rings and Modules, Volume 2

Algebras, Rings and Modules, Volume 2

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