Non-Unique Factorizations

This monograph-the first of its kind-presents the current state of knowledge on the theory of non-unique factorizations along with a broad discussion of its algebraic, combinatorial, and analytic fundamentals. The book focuses on factorization properties in rings of integers, orders of algebraic number fields, holomorphy rings, Krull and Mori domains, Krull monoids, congruence monoids, Hilbert monoids, and zero-sum sequences over Abelian groups. It also includes self-contained introductions to the v-ideal theory of monoids, additive group theory, and abstract analytic number theory. Within this treatment, the authors unify, extend, and put into a new context many known algebraic, combinatorial, and analytic results.