The reflexive property for rings was introduced by Mason and play roles in noncommutative ring theory. A ring R is called reflexive if for \(a, b \in R\), \(aRb = 0\) implies \(bRa = 0\). Recently, Kheradmand et al. introduced the notion of RNP (reflexive-nilpotents-property) rings by restricting the reflexive property to nilpotent elements. In this article, we study reflexive-nilpotents-property skewed by a ring endomorphism \(\alpha \) and introduce the notion of \(\alpha \)-skew RNP rings. We investigate various properties and extensions of these rings and also determine the structure of minimal noncommutative \(\alpha \)-skew RNP rings.

中文翻译：

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环内同态偏向的自反幂等性质

环的反射性是梅森（Mason）引入的，并在非交换环理论中起作用。如果对于\（a，b \ in R \），\（aRb = 0 \）意味着\（bRa = 0 \），则将环R称为自反。最近，Kheradmand等人。通过将反射性限制在幂等元素上，介绍了RNP（反射性幂等性质）环的概念。在本文中，我们研究由环内同态\（\ alpha \）倾斜的自反幂幂性质，并介绍\（\ alpha \）-倾斜RNP环的概念。我们研究了这些环的各种性质和扩展，并确定了最小非交换\（\ alpha \）-倾斜RNP环的结构。