Prime divisors and noncommutative valuation theory
Classical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves. But the noncommutative equivalent is mainly applied to finite dimensional skewfields. Recently however, new types of algebras have become popul...
Guardat en:
| Autors principals: | , , |
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| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edició: | 1st ed. 2012. |
| Col·lecció: | Lecture notes in Mathermatics
2059 |
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 224 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Prime divisors and noncommutative valuation theory, Hidethoshi Marubayashi, Freddy van Oystaeyen, Berlin, Springer, 2012, 1 vol. (IX-218 p.), Lecture notes in mathematics, 978-3-642-31151-2 • Prime divisors and noncommutative valuation theory, Hidethoshi Marubayashi, Freddy van Oystaeyen, Berlin, Springer, 2012, 1 vol. (IX-218 p.), Lecture notes in mathematics, 978-3-642-31151-2 • Prime Divisors and Noncommutative Valuation Theory, Texte imprimé, 9783642311536 |
| Sumari: | Classical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves. But the noncommutative equivalent is mainly applied to finite dimensional skewfields. Recently however, new types of algebras have become popular in modern algebra; Weyl algebras, deformed and quantized algebras, quantum groups and Hopf algebras, etc. The advantage of valuation theory in the commutative case is that it allows effective calculations, bringing the arithmetical properties of the ground field into the picture. This arithmetical nature is also present in the theory of maximal orders in central simple algebras. Firstly, we aim at uniting maximal orders, valuation rings, Dubrovin valuations, etc. in a common theory, the theory of primes of algebras. Secondly, we establish possible applications of the noncommutative arithmetics to interesting classes of algebras, including the extension of central valuations to nice classes of quantized algebras, the development of a theory of Hopf valuations on Hopf algebras and quantum groups, noncommutative valuations on the Weyl field and interesting rings of invariants and valuations of Gauss extensions |
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| Descripció de l’ítem: | L'impression du document génère 224 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografia: | Bibliogr. Index |
| ISBN: | 9783642311529 |
| ISSN: | 1617-9692 |
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