Abstract
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.
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Bhattacharjee, A. Reflexive-nilpotents-property skewed by ring endomorphisms. Arab. J. Math. 9, 63–72 (2020). https://doi.org/10.1007/s40065-018-0229-1
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DOI: https://doi.org/10.1007/s40065-018-0229-1