A01=Alfred Geroldinger
A01=Franz Halter-Koch
abelian
Abelian Groups
Additive Abelian Group
additive group structure
advanced algebraic structures
algebraic
Algebraic Number Field
analytic number theory
arithmetical invariants
Author_Alfred Geroldinger
Author_Franz Halter-Koch
Block Monoids
Category=PBH
Completely Integrally Closed
complex analysis methods
Congruence Monoids
Cross Number
dedekind
Dedekind Domain
Divisor Theory
domain
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Factorial Monoid
factorization theory
field
Finitary Monoids
finite
Finite Abelian Group
Finite Class Group
Finite Non-empty Subset
Free Monoid
group
Integral Domains
Invertible Fractional Ideal
krull
Krull Domain
Krull Monoid
Maximal Ideals
monoid
Noetherian Domains
Non-unique Factorizations
number
polyhedral cone applications
Prime Power Order
Reduced Krull Monoid
Tamely Generated
Product details
- ISBN 9781584885764
- Weight: 1451g
- Dimensions: 178 x 254mm
- Publication Date: 13 Jan 2006
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factorizations: Algebraic, Combinatorial, and Analytic Theory offers a look at the present state of the theory in a single, unified resource.
Taking a broad look at the algebraic, combinatorial, and analytic fundamentals, this book derives factorization results and applies them in concrete arithmetical situations using appropriate transfer principles. It begins with a basic introduction that can be understood with knowledge of standard basic algebra. The authors then move to the algebraic theory of monoids, arithmetic theory of monoids, the structure of sets of lengths, additive group theory, arithmetical invariants, and the arithmetic of Krull monoids. They also provide a self-contained introduction to abstract analytic number theory as well as a modern treatment of W. Narkiewicz's analytic theory of non-unique factorizations.
Non-Unique Factorizations: Algebraic, Combinatorial, and Analytic Theory builds the discussion from first principles to applied problem solving, making it ideally suited to those not familiar with the theory as well as those who wish to deepen their understanding.
Alfred Geroldinger, Franz Halter-Koch
