[EAN: 9780387904214], Neubuch, [PU: Springer New York Nov 1979], MATHEMATIK; ABELIANGROUP; ALGEBRA; ALGEBRAICSTRUCTURE; DERIVATION; FINITE; GRUPPENSCHEMA; INVARIANT; MORPHISM; TOPOLOGY; F… Mehr…
[EAN: 9780387904214], Neubuch, [PU: Springer New York Nov 1979], MATHEMATIK; ABELIANGROUP; ALGEBRA; ALGEBRAICSTRUCTURE; DERIVATION; FINITE; GRUPPENSCHEMA; INVARIANT; MORPHISM; TOPOLOGY; FUNCTION; PROOF; THEOREM, This item is printed on demand - it takes 3-4 days longer - Neuware -Ah Love! Could you and I with Him consl ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme. 180 pp. Englisch, Books<
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*Introduction to Affine Group Schemes* - Auflage 1979 / gebundene Ausgabe für 90.99 € / Aus dem Bereich: Bücher, Wissenschaft, Mathematik Medien > Bücher nein Buch (gebunden) Hardcover;Na… Mehr…
*Introduction to Affine Group Schemes* - Auflage 1979 / gebundene Ausgabe für 90.99 € / Aus dem Bereich: Bücher, Wissenschaft, Mathematik Medien > Bücher nein Buch (gebunden) Hardcover;Naturwissenschaften, Medizin, Informatik, Technik;Arithmetik, Algebra, Springer New York<
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[EAN: 9780387904214], Neubuch, [PU: Springer New York Nov 1979], MATHEMATIK; ABELIANGROUP; ALGEBRA; ALGEBRAICSTRUCTURE; DERIVATION; FINITE; GRUPPENSCHEMA; INVARIANT; MORPHISM; TOPOLOGY; F… Mehr…
[EAN: 9780387904214], Neubuch, [PU: Springer New York Nov 1979], MATHEMATIK; ABELIANGROUP; ALGEBRA; ALGEBRAICSTRUCTURE; DERIVATION; FINITE; GRUPPENSCHEMA; INVARIANT; MORPHISM; TOPOLOGY; FUNCTION; PROOF; THEOREM, This item is printed on demand - it takes 3-4 days longer - Neuware -Ah Love! Could you and I with Him consl ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme. 180 pp. Englisch, Books<
NEW BOOK. Versandkosten: EUR 24.78 BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany [57449362] [Rating: 4 (von 5)]
[EAN: 9780387904214], Neubuch, [SC: 35.55], [PU: Springer New York], MATHEMATIK; ABELIANGROUP; ALGEBRA; ALGEBRAICSTRUCTURE; DERIVATION; FINITE; GRUPPENSCHEMA; INVARIANT; MORPHISM; TOPOLOGY; FUNCTION; PROOF; THEOREM, Druck auf Anfrage Neuware - Printed after ordering - Ah Love! Could you and I with Him consl ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme., Books<
*Introduction to Affine Group Schemes* - Auflage 1979 / gebundene Ausgabe für 90.99 € / Aus dem Bereich: Bücher, Wissenschaft, Mathematik Medien > Bücher nein Buch (gebunden) Hardcover;Na… Mehr…
*Introduction to Affine Group Schemes* - Auflage 1979 / gebundene Ausgabe für 90.99 € / Aus dem Bereich: Bücher, Wissenschaft, Mathematik Medien > Bücher nein Buch (gebunden) Hardcover;Naturwissenschaften, Medizin, Informatik, Technik;Arithmetik, Algebra, Springer New York<
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Ah Love! Could you and I with Him consl?ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme.
Detailangaben zum Buch - Introduction to Affine Group Schemes
EAN (ISBN-13): 9780387904214 ISBN (ISBN-10): 0387904212 Gebundene Ausgabe Taschenbuch Erscheinungsjahr: 2007 Herausgeber: Springer New York 180 Seiten Gewicht: 0,438 kg Sprache: eng/Englisch
Buch in der Datenbank seit 2008-02-23T07:59:50+01:00 (Vienna) Detailseite zuletzt geändert am 2024-02-16T15:20:07+01:00 (Vienna) ISBN/EAN: 0387904212
ISBN - alternative Schreibweisen: 0-387-90421-2, 978-0-387-90421-4 Alternative Schreibweisen und verwandte Suchbegriffe: Autor des Buches: waterhouse william Titel des Buches: introduction affine group schemes, äffin, group zero, graduate text mathematics, the group, waterhouse, graduate texts mathematics
Daten vom Verlag:
Autor/in: W.C. Waterhouse Titel: Graduate Texts in Mathematics; Introduction to Affine Group Schemes Verlag: Springer; Springer US 164 Seiten Erscheinungsjahr: 1979-11-13 New York; NY; US Sprache: Englisch 90,94 € (DE) 93,49 € (AT) 100,50 CHF (CH) Available XII, 164 p.
BB; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Gruppen und Gruppentheorie; Verstehen; Abelian group; Algebra; Algebraic structure; Derivation; Finite; Gruppenschema; Invariant; Morphism; Topology; function; proof; theorem; Group Theory and Generalizations; Algebra; Algebra; BC
I The Basic Subject Matter.- 1 Affine Group Schemes.- 2 Affine Group Schemes: Examples.- 3 Representations.- 4 Algebraic Matrix Groups.- II Decomposition Theorems.- 5 Irreducible and Connected Components.- 6 Connected Components and Separable Algebras.- 7 Groups of Multiplicative Type.- 8 Unipotent Groups.- 9 Jordan Decomposition.- 10 Nilpotent and Solvable Groups.- III The Infinitesimal Theory.- 11 Differentials.- 12 Lie Algebras.- IV Faithful Flatness and Quotients.- 13 Faithful Flatness.- 14 Faithful Flatness of Hopf Algebras.- 15 Quotient Maps.- 16 Construction of Quotients.- V Descent Theory.- 17 Descent Theory Formalism.- 18 Descent Theory Computations.- Appendix: Subsidiary Information.- A.1 Directed Sets and Limits.- A.2 Exterior Powers.- A.3 Localization. Primes, and Nilpotents.- A.4 Noetherian Rings.- A.5 The Hilbert Basis Theorem.- A.6 The Krull Intersection Theorem.- A.7 The Nocthcr Normalization Lemma.- A.8 The Hilbert Nullstellensatz.- A.9 Separably Generated Fields.- A.10 Rudimentary Topological Terminology.- Further Reading.- Index of Symbols.
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