论文标题
加权Erdős-Burgess and Davenport Constant in Commutative Rings
Weighted Erdős-Burgess and Davenport constant in commutative rings
论文作者
论文摘要
让$ r $为有限的统一戒指。 $ r $中的iDempotent是$ e $ in $ e^2 = e $的元素$ e \。令$ψ$为$ r $的所有自动形态的组$ {\ rm aut}（r）$的子组。 $ψ-$加权erdős-burgess常数$ {\ rm i}_ψ（r）$定义为最小的正整数$ \ ell $，以使得每个序列上的每个序列至少$ \ ell $都必须包含一个非公开的$ a_1 $ a_1，\ ldots，\ ldots $ a_ port y a_ a_ a_ a_ fim for ψ_i（a_i）$是$ r $的一个同上，其中$ψ_1，\ ldots，ψ_r\ inψ$。在本文中，对于Dedekind域$ r $的有限商环，在$ R $的$ψ-$加权erd-burgess常数与$ c $ r $的$ψ-$加权的davenport常数之间建立了连接。
Let $R$ be a finite commutative unitary ring. An idempotent in $R$ is an element $e\in R$ with $e^2=e$. Let $Ψ$ be a subgroup of the group ${\rm Aut}(R)$ of all automorphisms of $R$. The $Ψ-$weighted Erdős-Burgess constant ${\rm I}_Ψ(R)$ is defined as the smallest positive integer $\ell$ such that every sequence over $R$ of length at least $\ell$ must contain a nonempty subsequence $a_1,\ldots, a_{r}$ such that $\prod\limits_{i=1}^r ψ_i(a_i)$ is one idempotent of $R$ where $ψ_1,\ldots,ψ_r\in Ψ$. In this paper, for the finite quotient ring of a Dedekind domain $R$, a connection is established between the $Ψ-$weighted-Erdős-Burgess constant of $R$ and the $Ψ-$weighted Davenport constant of its group of units by all the prime ideals of $R$.
