Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 3

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

The set of minimal distances in Krull monoids

100%
Geroldinger A., Zhong Q.
Acta Arithmetica
|
2016
|
tom 173
|
nr 2
97-120
EN
Let H be a Krull monoid with class group G. Then every nonunit a ∈ H can be written as a finite product of atoms, say $a= u_1 · ... · u_k$. The set 𝖫(a) of all possible factorization lengths k is called the set of lengths of a. If G is finite, then there is a constant M ∈ ℕ such that all sets of lengths are almost arithmetical multiprogressions with bound M and with difference d ∈ Δ*(H), where Δ*(H) denotes the set of minimal distances of H. We show that max Δ*(H) ≤ max{exp(G)-2,𝗋(G)-1} and that equality holds if every class of G contains a prime divisor, which holds true for holomorphy rings in global fields.
2
Content available remote

Subsequence sums of zero-sum free sequences over finite abelian groups

81%
Qu Y., Xia X., Xue L., Zhong Q.
Colloquium Mathematicum
|
2015
|
tom 140
|
nr 1
119-127
EN
Let G be a finite abelian group of rank r and let X be a zero-sum free sequence over G whose support supp(X) generates G. In 2009, Pixton proved that $|Σ(X)| ≥ 2^{r-1}(|X|-r+2) - 1$ for r ≤ 3. We show that this result also holds for abelian groups G of rank 4 if the smallest prime p dividing |G| satisfies p ≥ 13.
3
Content available remote

A quantitative aspect of non-unique factorizations: the Narkiewicz constants III

81%
Gao W., Peng J., Zhong Q.
Acta Arithmetica
|
2013
|
tom 158
|
nr 3
271-285
EN
Let K be an algebraic number field with non-trivial class group G and $𝓞_K$ be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let $F_k(x)$ denote the number of non-zero principal ideals $a𝓞_K$ with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that $F_k(x)$ behaves for x → ∞ asymptotically like $x(log x)^{1-1/|G|} (log log x)^{𝖭_k (G)}$. We prove, among other results, that $𝖭₁(C_{n₁} ⊕ C_{n₂}) = n₁ + n₂$ for all integers n₁,n₂ with 1 < n₁|n₂.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.