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- W4289762970 abstract "An ideal $I$ of a ring $R$ is called left N-reflexive if for any $ain$ nil$(R)$, $bin R$, being $aRb subseteq I$ implies $bRa subseteq I$ where nil$(R)$ is the set of all nilpotent elements of $R$. The ring $R$ is called left N-reflexive if the zero ideal is left N-reflexive. We study the properties of left N-reflexive rings and related concepts. Since reflexive rings and reduced rings are left N-reflexive, we investigate the sufficient conditions for left N-reflexive rings to be reflexive and reduced. We first consider basic extensions of left N-reflexive rings. For an ideal-symmetric ideal $I$ of a ring $R$, $R/I$ is left N-reflexive. If an ideal $I$ of a ring $R$ is reduced as a ring without identity and $R/I$ is left N-reflexive, then $R$ is left N-reflexive. If $R$ is a quasi-Armendariz ring and the coefficients of any nilpotent polynomial in $R[x]$ are nilpotent in $R$, it is proved that $R$ is left N-reflexive if and only if $R[x]$ is left N-reflexive. We show that the concept of N-reflexivity is weaker than that of reflexivity and stronger than that of left N-right idempotent reflexivity and right idempotent reflexivity which are introduced in Section 5." @default.
- W4289762970 created "2022-08-04" @default.
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- W4289762970 date "2018-07-06" @default.
- W4289762970 modified "2023-09-25" @default.
- W4289762970 title "Reflexivity of Rings via Nilpotent Elements" @default.
- W4289762970 doi "https://doi.org/10.48550/arxiv.1807.02333" @default.
- W4289762970 hasPublicationYear "2018" @default.
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