Contains chapters that demonstrate the diversity of approaches taken in studying nonunique factorizations and serve both as an introduction to factorization theory and as a survey of trends and results. This book also provides chapters that show research motivated by arithmetical properties of commutative rings and monoids.

Preface 1 Non-Atomic Unique Factorization in Integral Domains 2 Divisibility Properties in Graded Integral Domains 3 Extensions of Half-Factorial Domains: A Survey 4 C-Monoids and Congruence Monoids in Krull Domains 5 Monotone Chains of Factorizations in C-Monoids 6 Transfer Principles in the Theory of Non-unique Factorizations 7 Cale Monoids, Cale Domains, and Cale Varieties 8 Weakly Krull Inside Factorial Domains 9 The m-Complement of a Multiplicative Set 10 Some Remarks on Infinite Products 11 Rings with Prime Nilradical 12 On the Ideal Generated by the Values of a Polynomial 13 Using Factorizations to Prove a Partition Identity 14 On Inside Factorial Integral Domains 15 Polynomial Separation of Points in Algebras 16 k-Factorized Elements in Telescopic Numerical Semigroups 17 Prufer Conditions in Rings with Zero-Divisors 18 Unmixedness and the Generalized Principal Ideal Theorem 19 A Note on Sets of Lengths of Powers of Elements of Finitely Generated Monoids 20 UMV-Domains 21 On Local Half-Factorial Orders 22 On Factorization in Krull Domains with Divisor Class Group Z2k 23 Integral Morphisms 24 A Special Type of Invertible Ideal 25 Factorization into Radical Ideals 26 Strongly Primary Ideals