Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory free download
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.
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