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Titlebook: Basic Notions of Algebra; Igor R. Shafarevich Book 2005 Springer-Verlag Berlin Heidelberg 2005 Category theory.Group representation.Group

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期刊全称Basic Notions of Algebra
影响因子2023Igor R. Shafarevich
视频video
学科分类Encyclopaedia of Mathematical Sciences
图书封面Titlebook: Basic Notions of Algebra;  Igor R. Shafarevich Book 2005 Springer-Verlag Berlin Heidelberg 2005 Category theory.Group representation.Group
影响因子§22. K-theory 230 A. Topological X-theory 230 Vector bundles and the functor Vec(X). Periodicity and the functors KJX). K(X) and t the infinite-dimensional linear group. The symbol of an elliptic differential operator. The index theorem. B. Algebraic K-theory 234 The group of classes of projective modules. K , K and K of a ring. K of a field and o l n 2 its relations with the Brauer group. K-theory and arithmetic. Comments on the Literature 239 References 244 Index of Names 249 Subject Index 251 Preface This book aims to present a general survey of algebra, of its basic notions and main branches. Now what language should we choose for this? In reply to the question ‘What does mathematics study?‘, it is hardly acceptable to answer ‘structures‘ or ‘sets with specified relations‘; for among the myriad conceivable structures or sets with specified relations, only a very small discrete subset is of real interest to mathematicians, and the whole point of the question is to understand the special value of this infinitesimal fraction dotted among the amorphous masses. In the same way, the meaning of a mathematical notion is by no means confined to its formal definition; in fact, it may be
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Algebraic Aspects of Dimension,s, which are a direct generalisation of vector spaces, there are analogous notions, which play the same fundamental role. On the other hand, we have considered algebraic curves, surfaces, and so on, and have ‘coordinatised’ each such object . by assigning to it the coordinate ring .[.] or the ration
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Examples of Groups: Infinite Discrete Groups,ally arise. Usually the infinite set of elements of a group is defined by some constructive process or formula. This formula may contain some parameters, which may take integer values, or be real numbers, or even points of a manifold. This is the starting point of an informal classification: groups
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Group Representations,losely related to the idea of ‘coordinatisation’. The meaning of coordinatisation is to specify objects forming a homogeneous set . by assigning individually distinguishable quantities to them. Of course such a specification is in principle impossible: considering the inverse map would then make the
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https://doi.org/10.1007/b137643Category theory; Group representation; Group theory; K-theory; algebra; associative algebra; category; coho
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