发表机构
National University of Singapore（新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明约化非McCoy环仅当n=2时可同时满足零化子条件与$(A_n)$，通过构造可数例子并证明$(A_3)$与零化子条件迫使环为McCoy环。
AI 中文摘要
有人曾问：一个约化非McCoy环是否可能同时满足零化子条件和某个$n \geq 2$的$(A_n)$性质。本文证明，此类环恰好当$n=2$时存在，我们构造了一个可数例子，并表明零化子条件与$(A_3)$共同迫使环成为McCoy环。
英文摘要
It has been asked whether a reduced non-McCoy ring can satisfy both the annihilator condition and $(A_n)$ for some $n \geq 2$. In this work, we prove that such rings exist exactly when $n=2$, by constructing a countable example and showing that the annihilator condition together with $(A_3)$ forces a ring to be McCoy.
