| Title:
|
The tame degree and related invariants of non-unique factorizations (English) |
| Author:
|
Halter-Koch, Franz |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
16 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
57-68 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Local tameness and the finiteness of the catenary degree are two crucial finiteness conditions in the theory of non-unique factorizations in monoids and integral domains. In this note, we refine the notion of local tameness and relate the resulting invariants with the usual tame degree and the $\omega $-invariant. Finally we present a simple monoid which fails to be locally tame and yet has nice factorization properties. (English) |
| Keyword:
|
Non-unique factorizations |
| Keyword:
|
tame degree |
| Keyword:
|
atomic monoids |
| MSC:
|
13A05 |
| MSC:
|
20M14 |
| idZBL:
|
Zbl 1196.13005 |
| idMR:
|
MR2498637 |
| . |
| Date available:
|
2009-12-29T09:24:26Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137501 |
| . |
| Reference:
|
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| Reference:
|
[2] Gao W., Geroldinger A.: On products of k-atoms.. Monatsh. Math., to appear. Zbl 1184.20051, MR 2488859 |
| Reference:
|
[3] Geroldinger A., Halter-Koch F.: Non-Unique Factorizations.. Algebraic, Combinatorial and Analytic Theory. Chapman & Hall/CRC, 2006. Zbl 1117.13004, MR 2194494 |
| Reference:
|
[4] Geroldinger A., Halter-Koch F.: Non-Unique Factorizations: A Survey.. Multiplicative Ideal Theory in Commutative Algebra, J.W. Brewer, S. Glaz, W. Heinzer, and B. Olberding (eds.), pp. 217–226, Springer 2006. Zbl 1117.13004, MR 2265810 |
| Reference:
|
[5] Geroldinger A., Hassler W.: Local tameness of $v$-noetherian monoids., J. Pure Appl. Algebra 212 (2008), 1509–1524. Zbl 1133.20047, MR 2391663, 10.1016/j.jpaa.2007.10.020 |
| Reference:
|
[6] Geroldinger A., Hassler W.: Arithmetic of Mori domains and monoids., J. Algebra 319 (2008), 3419–3463. Zbl 1195.13022, MR 2408326, 10.1016/j.jalgebra.2007.11.025 |
| Reference:
|
[7] Halter-Koch F.: Non-Unique factorizations of algebraic integers., Funct. Approx., to appear. Zbl 1217.11096, MR 2490087 |
| . |
