Previous |  Up |  Next


Non-unique factorizations; tame degree; atomic monoids
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.
[1] Anderson D. F.: Elasticity of factorizations in integral domains: a survey. Factorization in Integral Domains, D. D. Anderson (ed.), pp. 1–29, Marcel Dekker, 1997 MR 1460767 | Zbl 0903.13008
[2] Gao W., Geroldinger A.: On products of k-atoms. Monatsh. Math., to appear. MR 2488859 | Zbl 1184.20051
[3] Geroldinger A., Halter-Koch F.: Non-Unique Factorizations. Algebraic, Combinatorial and Analytic Theory. Chapman & Hall/CRC, 2006. MR 2194494 | Zbl 1117.13004
[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. MR 2265810 | Zbl 1117.13004
[5] Geroldinger A., Hassler W.: Local tameness of $v$-noetherian monoids. J. Pure Appl. Algebra 212 (2008), 1509–1524. DOI 10.1016/j.jpaa.2007.10.020 | MR 2391663 | Zbl 1133.20047
[6] Geroldinger A., Hassler W.: Arithmetic of Mori domains and monoids. J. Algebra 319 (2008), 3419–3463. DOI 10.1016/j.jalgebra.2007.11.025 | MR 2408326 | Zbl 1195.13022
[7] Halter-Koch F.: Non-Unique factorizations of algebraic integers. Funct. Approx., to appear. MR 2490087 | Zbl 1217.11096
Partner of
EuDML logo