Abstract The rings for which any polynomial with a nonzero right annihilator must have a nonzero constant right annihilator are called the right McCoy rings. This class of rings includes the duo, reversible, polynomially semicommutative, and Armendariz rings, among others. In this paper we introduce a new condition, strictly generalizing the reversible property, which still implies the McCoy condition. We call this new condition the outer McCoy property; it arises from guaranteeing annihilators in unexpected places. This outer McCoy condition is further motivated by a property of 2-primal rings, which we call the Camillo property, first noticed by Victor Camillo and the fourth author. We study the relationships between the outer McCoy property, the Camillo property, and other standard ring-theoretic conditions, with many examples delimiting their connections. For instance, we show that any ring whose set of nilpotents is closed under multiplication must satisfy the Camillo property when restricted to linear polynomials.

中文翻译：

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零除数放置、Camillo 的条件和 McCoy 属性

摘要 任何具有非零右消灭子的多项式必须有一个非零常数右消灭子的环称为右McCoy环。此类环包括二重环、可逆环、多项式半交换环和 Armendariz 环等。在本文中，我们引入了一个新条件，严格概括了可逆性质，这仍然意味着 McCoy 条件。我们称这种新条件为外部 McCoy 属性；它源于在意想不到的地方保证歼灭者。这种外部 McCoy 条件进一步受到 2-primal 环的性质的推动，我们称之为 Camillo 性质，首先由 Victor Camillo 和第四作者注意到。我们研究了外部 McCoy 性质、Camillo 性质和其他标准环论条件之间的关系，用许多例子来界定它们的联系。例如，我们表明，当限制为线性多项式时，任何幂零集在乘法下闭合的环都必须满足卡米洛性质。