I.R. Shafarevich's Books

Basic Algebraic Geometry

By: I.R. Shafarevich

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Algebraic geometry occupied a central place in the mathematics of the last century. The deepest results of Abel, Riemann, Weierstrass, many of the most important papers of Klein and Poincare belong to this do mam. At the end of the last and the beginning of the present century the attitude towards algebraic geometry changed abruptly. Around 1910 Klein wrote: "When I was a student, Abelian functions*-as an after-effect of Jacobi's tradition-were regarded as the undIsputed summit of mathe matics, and each of us, as a matter of course, had the ambition to forge ahead in this field. And now? The young generation hardly know what Abelian functions are." (Vorlesungen tiber die Entwicklung der Mathe matik im XIX. Jahrhundert, Springer-Verlag, Berlin 1926, Seite 312). The style of thinking that was fully developed in algebraic geometry at that time was too far removed from the set-theoretical and axio matic spirit, which then determined the development of mathematics. Several decades had to lapse before the rise of the theory of topolo gical, differentiable and complex manifolds, the general theory of fields, the theory of ideals in sufficiently general rings, and only then it became possible to construct algebraic geometry on the basis of the principles of set-theoretical mathematics. Around the middle of the present century algebraic geometry had undergone to a large extent such a reshaping process. As a result, it can again lay claim to the position it once occupied in mathematics

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450

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Springer Science & Business Media

Published Date

ISBN 10

3642962009

ISBN 13

9783642962004

Algebraic Geometry IV

Linear Algebraic Groups Invariant Theory

By: A.N. Parshin,I.R. Shafarevich

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Algebraic Geometry IV

Linear Algebraic Groups Invariant Theory

By: A.N. Parshin,I.R. Shafarevich

Two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory, by well-known experts in the fields. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.

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304

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Springer Science & Business Media

Published Date

ISBN 10

3540546820

ISBN 13

9783540546825

Algebraic Geometry II

Cohomology of Algebraic Varieties. Algebraic Surfaces

By: I.R. Shafarevich

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Algebraic Geometry II

Cohomology of Algebraic Varieties. Algebraic Surfaces

By: I.R. Shafarevich

This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.

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282

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Springer Science & Business Media

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ISBN 10

3540546804

ISBN 13

9783540546801

Algebra II

Noncommutative Rings Identities

By: A.I. Kostrikin,I.R. Shafarevich

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Algebra II

Noncommutative Rings Identities

By: A.I. Kostrikin,I.R. Shafarevich

The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the best-known example of a non-commutative alge 1 bra • Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of non-commutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry - for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with· polynomial coefficients) often appears in the representation theory of Lie algebras. In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the so-called microlocal analysis. The theory of operator algebras (Le.

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241

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Springer Science & Business Media

Published Date

ISBN 10

3642728995

ISBN 13

9783642728990

Algebra IV

Infinite Groups. Linear Groups

By: A.I. Kostrikin,I.R. Shafarevich

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Algebra IV

Infinite Groups. Linear Groups

By: A.I. Kostrikin,I.R. Shafarevich

Group theory is one of the most fundamental branches of mathematics. This highly accessible volume of the Encyclopaedia is devoted to two important subjects within this theory. Extremely useful to all mathematicians, physicists and other scientists, including graduate students who use group theory in their work.

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Page Count

210

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Springer Science & Business Media

Published Date

ISBN 10

3662028697

ISBN 13

9783662028698

Book's by I.R. Shafarevich

Basic Algebraic Geometry

Basic Algebraic Geometry

Algebraic Geometry IV

Algebraic Geometry IV

Algebraic Geometry II

Algebraic Geometry II

Algebra II

Algebra II

Algebra IV

Algebra IV

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