One-sided duo property on nilpotents

Temel Bulgular & Veri:We prove the following for a one-sided nilpotent-duo ring $R$: (i) The set of nilpotents in $R$ forms a subring; (ii) Köthe's conjecture holds for $R$; (iii) the subring generated by the identity and the set of nilpotents in $R$ is a one-sided duo ring; (iv) if the polynomial ring $R[x]$ over $R$ is one-sided nilpotent-duo then the set of nilpotents in $R$ forms a commutative ring, and $R[x]$ is an NI ring.

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Sonuç & Katkı:Especially we investigate several kinds of conditions under which one-sided nilpotent-duo rings are NI.

🔬Tür:Araştırma Makalesi

📍Kapsam:Genişletilmiş Akademik Örneklem

⚙️Değişkenler:right (left) nilpotent-duo ring · nilpotent · right (left) duo ring

Abstract

We study the structure of nilpotents in relation with a ring property that is near to one-sided duo rings. Such a property is said to be one-sided nilpotent-duo. We prove the following for a one-sided nilpotent-duo ring $R$: (i) The set of nilpotents in $R$ forms a subring; (ii) Köthe's conjecture holds for $R$; (iii) the subring generated by the identity and the set of nilpotents in $R$ is a one-sided duo ring; (iv) if the polynomial ring $R[x]$ over $R$ is one-sided nilpotent-duo then the set of nilpotents in $R$ forms a commutative ring, and $R[x]$ is an NI ring. Several connections between one-sided nilpotent-duo and one-sided duo are given. The structure of one-sided nilpotent-duo rings is also studied in various situations in ring theory. Especially we investigate several kinds of conditions under which one-sided nilpotent-duo rings are NI.

Anahtar kelimeler

right (left) nilpotent-duo ring nilpotent right (left) duo ring radical NI ring matrix ring ascending chain condition on left (right) annihilators

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Bu Makaleye Atıf Yap

Kim, N. K., Lee, Y., Hong, C. Y., Kim, H. K., Kwak, T. K. (2022). One-sided duo property on nilpotents. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 6, 1974–1987. https://ajindex.com/articles/529616

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