<電子ブック>
Prime Divisors and Noncommutative Valuation Theory / by Hidetoshi Marubayashi, Fred Van Oystaeyen
(Lecture Notes in Mathematics. ISSN:16179692 ; 2059)
版 | 1st ed. 2012. |
---|---|
出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
出版年 | 2012 |
大きさ | IX, 218 p : online resource |
著者標目 | *Marubayashi, Hidetoshi author Van Oystaeyen, Fred author SpringerLink (Online service) |
件 名 | LCSH:Algebra LCSH:Geometry LCSH:Algebraic geometry LCSH:Associative rings LCSH:Associative algebras FREE:Algebra FREE:Geometry FREE:Algebraic Geometry FREE:Associative Rings and Algebras |
一般注記 | 1. General Theory of Primes -- 2. Maximal Orders and Primes -- 3. Extensions of Valuations to some Quantized Algebras 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 HTTP:URL=https://doi.org/10.1007/978-3-642-31152-9 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
|
Springer eBooks | 9783642311529 |
|
電子リソース |
|
EB00211014 |
類似資料
この資料の利用統計
このページへのアクセス回数:2回
※2017年9月4日以降