Prime Divisors and Noncommutative Valuation Theory is popular PDF and ePub book, written by Hidetoshi Marubayashi in 2012-08-21, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Prime Divisors and Noncommutative Valuation Theory can be Read Online from any device for your convenience.
Prime Divisors and Noncommutative Valuation Theory Book PDF Summary
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.
Detail Book of Prime Divisors and Noncommutative Valuation Theory PDF
- Author : Hidetoshi Marubayashi
- Release : 21 August 2012
- Publisher : Springer
- ISBN : 9783642311529
- Genre : Mathematics
- Total Page : 225 pages
- Language : English
- PDF File Size : 7,6 Mb
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