Some Characterizations of Krull Monoids

• 来源期刊: 代数集刊(英文版)
• 关键词: r-factorable monoid unique r-factorable monoid Krull monoid r-idealsystem
• 年，卷（期）: 2007,（3）
• 页码范围: 469-477
• 页数: 9页
• 语种: 英文

摘要

In this paper,Kaplansky-type theorems are given to characterize GCD-monoids and valuation monoids.Also,(unique) r-factorable monoids are defined and it is shown that S is a Krull monoid if and only if S is a unique t-factorable (resp.,w-factorable)monoid if and only if S is a t-factorable (resp.,w-factorable) t-Pr(u)fer monoid.