论文标题
在加权零和序列的单体上，并应用于galois数字和二元二元形式中的norm sonoids
On monoids of weighted zero-sum sequences and applications to norm monoids in Galois number fields and binary quadratic forms
论文作者
论文摘要
令$ g $为添加剂有限的阿贝里安组和$γ\ subset \ permatatorName {end}（g）$是$ g $的内态组的子集。 $ s = g_1 \ cdot \ ldots \ cdot g _ {\ ell} $上的$ g $上的$是（$γ$ - ）加权零和序列，如果$γ_1，\ ldots，γ_{\ ell} （g _ {\ ell}）= 0 $。我们构建了从标准单型（带有Galois组$γ$的Galois代数数字字段）的同态传递同态，并从以二元二元形式为代表的正整数的单型，到加权零-MUM序列的单体。然后，我们研究加权零和序列的单体代数和算术特性。
Let $G$ be an additive finite abelian group and $Γ\subset \operatorname{End} (G)$ be a subset of the endomorphism group of $G$. A sequence $S = g_1 \cdot \ldots \cdot g_{\ell}$ over $G$ is a ($Γ$-)weighted zero-sum sequence if there are $γ_1, \ldots, γ_{\ell} \in Γ$ such that $γ_1 (g_1) + \ldots + γ_{\ell} (g_{\ell})=0$. We construct transfer homomorphisms from norm monoids (of Galois algebraic number fields with Galois group $Γ$) and from monoids of positive integers, represented by binary quadratic forms, to monoids of weighted zero-sum sequences. Then we study algebraic and arithmetic properties of monoids of weighted zero-sum sequences.
