Arithmetic of seminormal weakly Krull monoids and domains

被引：32

作者：

Geroldinger, Alfred ^{[1
]}

Kainrath, Florian ^{[1
]}

Reinhart, Andreas ^{[1
]}

机构：

[1] Karl Franzens Univ Graz, Inst Math & Wissensch Rechnen, NAWI Graz, A-8010 Graz, Austria

来源：

JOURNAL OF ALGEBRA | 2015年 / 444卷

基金：

奥地利科学基金会;

关键词：

Non-unique factorizations; Sets of lengths; Half-factoriality; Weakly Krull domains; Seminormal domains; Non-principal orders; HALF-FACTORIAL DOMAINS; NUMBER-THEORY; RINGS; FACTORIZATIONS; EXTENSIONS; CLOSURE; CHAINS;

D O I：

10.1016/j.jalgebra.2015.07.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the arithmetic of seminormal v-noetherian weakly Krull monoids with nontrivial conductor which have finite class group and prime divisors in all classes. These monoids include seminormal orders in holomorphy rings in global fields. The crucial property of seminormality allows us to give precise arithmetical results analogous to the well-known results for Krull monoids having finite class group and prime divisors in each class. This allows us to show, for example, that unions of sets of lengths are intervals and to provide a characterization of half-factoriality. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：201 / 245

页数：45

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