On invariants related to non-unique factorizations in block monoids and rings of algebraic integers

Rok, strany: 2005, 21 - 37

Let $K$ be a number field, $R$ its ring of integers and $H$ the set of non-zero principal ideals of $R$. For each positive integer $k$ the set $B_k(H)\subset H$ denotes the set of principal ideals for which the associated block has at most $k$ different factorizations. For the counting functions associated to these sets asymptotic formulae are known. These formulae involve constants that just depend on the ideal class group $G$ of $R$. Starting from a known combinatorial description for these constants, we use tools from additive group theory, in particular the notion of Davenport's constant and a classical addition theorem, to investigate them. We determine their precise value in case $G$ is an elementary group or a cyclic group of prime power order. For arbitrary $G$ we derive (explicit) lower bounds.

ISO 690:

Schmid, W. 2005. On invariants related to non-unique factorizations in block monoids and rings of algebraic integers. In Mathematica Slovaca, vol. 55, no.1, pp. 21-37. 0139-9918.

APA:

Schmid, W. (2005). On invariants related to non-unique factorizations in block monoids and rings of algebraic integers. Mathematica Slovaca, 55(1), 21-37. 0139-9918.