论文标题
有限交换环的Erdős-燃烧常数的下限
Lower bound for the Erdős-Burgess constant of finite 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 \。与环$ r $相关的erdős-burgess常数是最小的正整数$ \ ell $，因此，对于任何给定的$ \ ell $元素（允许重复）$ r $，例如$ a_1，\ ldots，a _ {\ ell} \ {1,2，\ ldots，\ ell \} $带有$ \ prod \ limits_ {j} a_j $ as diadempotent。在本文中，我们在有限的统一单一环中给出了Erdős-Burgess常数的下限。结果统一了一些最近在此不变的定理。
Let $R$ be a finite commutative unitary ring. An idempotent in $R$ is an element $e\in R$ with $e^2=e$. The Erdős-Burgess constant associated with the ring $R$ is the smallest positive integer $\ell$ such that for any given $\ell$ elements (repetitions are allowed) of $R$, say $a_1,\ldots,a_{\ell}\in R$, there must exist a nonempty subset $J\subset \{1,2,\ldots,\ell\}$ with $\prod\limits_{j\in J} a_j$ being an idempotent. In this paper, we give a lower bound of the Erdős-Burgess constant in a finite commutative unitary ring in terms of all its maximal ideals, and prove that the lower bound is attained in some cases. The result unifies some recently obtained theorems on this invariant.
