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Prime Divisors and Noncommutative Valuation Theory : Lecture Notes in Mathematics - Hidetoshi Marubayashi

Prime Divisors and Noncommutative Valuation Theory

Lecture Notes in Mathematics

Paperback Published: 22nd August 2012
ISBN: 9783642311512
Number Of Pages: 218

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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.

1. General Theory of Primes.- 2. Maximal Orders and Primes.- 3. Extensions of Valuations to some Quantized Algebras

ISBN: 9783642311512
ISBN-10: 3642311512
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 218
Published: 22nd August 2012
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.25
Weight (kg): 0.33

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