The Monotone Catenary Degree of Krull Monoids
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- 作者：Alfred Geroldinger ; Pingzhi Yuan
- 关键词：11B13 ; 11P70 ; 13A05 ; 20M13 ; Non ; unique factorizations ; catenary degree ; Krull monoids
- 刊名：Results in Mathematics
- 出版年：2013
- 出版时间：June 2013
- 年：2013
- 卷：63
- 期：3-4
- 页码：999-1031
- 全文大小：444KB
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Pingzhi Yuan (2)
1. Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit?t Graz, Heinrichstrasse 36, 8010, Graz, Austria
2. School of Mathematics, South China Normal University, 510631, Guangzhou, People’s Republic of China - ISSN：1420-9012
文摘
Let H be a Krull monoid with finite class group G such that every class contains a prime divisor. The monotone catenary degree c mon (H) of H is the smallest integer m with the following property: for each ${a \in H}$ and each two factorizations z, z-of a with length |z| ≤?|z′|, there exist factorizations z?=?z 0, ... ,z k ?=?z-of a with increasing lengths—that is, |z 0| ≤?... ≤?|z k |—such that, for each ${i \in [1,k]}$ , z i arises from z i-1 by replacing at most m atoms from z i-1 by at most m new atoms. Up to now there was only an abstract finiteness result for c mon (H), but the present paper offers the first explicit upper and lower bounds for c mon (H) in terms of the group invariants of G.