## Arithmetical Properties of Commutative Rings and MonoidsThe study of nonunique factorizations of elements into irreducible elements in commutative rings and monoids has emerged as an independent area of research only over the last 30 years and has enjoyed a recent flurry of activity and advancement. This book presents the proceedings of two recent meetings that gathered key researchers from around the world to review recent major results. The first seven chapters demonstrate the diversity of approaches taken in studying nonunique factorizations and serve both as an introduction to factorization theory and as a survey of current trends and results. The remaining chapters reflect research motivated by arithmetical properties of commutative rings and monoids. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

1 | |

Divisibility Properties in Graded Integral Domains | 22 |

Extensions of HalfFactorial Domains A Survey | 46 |

CMonoids and Congruence Monoids in Krull Domains | 71 |

Monotone Chains of Factorizations in CMonoids | 99 |

Transfer Principles in the Theory of Nonunique Factorizations | 114 |

Cale Monoids Cale Domains and Cale Varieties | 142 |

Weakly Krull Inside Factorial Domains | 172 |

Polynomial Separation of Points in Algebras | 253 |

kFactorized Elements in Telescopic Numerical Semigroups | 260 |

Prufer Conditions in Rings with ZeroDivisors | 272 |

Unmixedness and the Generalized Principal Ideal Theorem | 282 |

A Note on Sets of Lengths of Powers of Elements of Finitely Generated Monoids | 293 |

UMVDomains | 304 |

On Local HalfFactorial Orders | 316 |

On Factorization in Krull Domains with Divisor Class Group Z2k | 325 |

The mComplement of a Multiplicative Set | 180 |

Some Remarks on Infinite Products | 188 |

Rings with Prime Nilradical | 198 |

On the Ideal Generated by the Values of a Polynomial | 213 |

Using Factorizations to Prove a Partition Identity | 226 |

On Inside Factorial Integral Domains | 233 |

### Other editions - View all

### Common terms and phrases

a e H abelian group arithmetical assume atomic Bézout domain C-monoid Cale basis Cale domain Cale monoid Cl(D closure comaximal Commutative Rings congruence monoids contained Corollary D. F. Anderson Dedekind domain defined definition denote divisor class group equivalent example exists factorial integral domain factorial monoid Geroldinger graded integral domain H-essential half-factorial domain Halter-Koch Hence homomorphism implies infinite product inside factorial integral integral morphisms integrally closed isomorphic Krull domain Krull monoid Lemma Let H Marcel Dekker Math Max(R maximal ideal minimal monoid H Nil(R nonnil nonzero nonunit numerical semigroup polynomial prime ideal principal ideal Proof Proposition Prüfer domain Pure Appl quotient field resp result root extension Section semigroup ring seminormal sets of lengths splitting set strongly primary subgroup submonoid Suppose t-ideal Theorem 3.1 upper to zero valuation domain wB-ht-unmixed wB-unmixed weakly factorial weakly Krull Zafrullah