| 书目名称 | Prime Divisors and Noncommutative Valuation Theory | | 编辑 | Hidetoshi Marubayashi,Fred Van Oystaeyen | | 视频video | | | 概述 | Describes different generalizations of valuations from the common generalized concept of primes in algebras.Combines the arithmetic of finite dimensional central simple algebras with new theory for in | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | 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 valu | | 出版日期 | Book 2012 | | 关键词 | 16W40, 16W70, 16S38, 16H10, 13J20, 16T05; Weyl field; filtration; order; valuation | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-31152-9 | | isbn_softcover | 978-3-642-31151-2 | | isbn_ebook | 978-3-642-31152-9Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer-Verlag Berlin Heidelberg 2012 |
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发表于 2025-3-21 19:41:14
