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Dergiler / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 1

Extensions and topological conditions of NJ rings

Yanli REN
Meimei JIANG
Yao WANG
Sayfa
44–62
Yayın Tarihi
2022-11-04
DOI
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Moreover, we consider some topological conditions for NJ rings and show for a NJ ring R that R is J-pm if and only if J - Spec(R) is a normal space if and only if Max(R) is a retract of J - Spec(R) .

📌 3 Maddede Bu Makale

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Amaç & Hipotez:A ring R is said to be NJ if J (R) = N (R) .
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Temel Bulgular & Veri:At the same time, we also prove that if R is a weakly 2-primal α -compatible ring with an isomorphism α of R , then R[x; α] is NJ; if R is a weakly 2-primal δ -compatible ring with a derivation δ of R , then R[x; δ] is NJ.
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Sonuç & Katkı:Moreover, we consider some topological conditions for NJ rings and show for a NJ ring R that R is J-pm if and only if J - Spec(R) is a normal space if and only if Max(R) is a retract of J - Spec(R) .
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

A ring R is said to be NJ if J (R) = N (R) . This paper mainly studies the relationship between NJ rings and related rings, and investigates the Dorroh extension, the Nagata extension, the Jordan extension, and some other extensions of NJ rings. At the same time, we also prove that if R is a weakly 2-primal α -compatible ring with an isomorphism α of R , then R[x; α] is NJ; if R is a weakly 2-primal δ -compatible ring with a derivation δ of R , then R[x; δ] is NJ. Moreover, we consider some topological conditions for NJ rings and show for a NJ ring R that R is J-pm if and only if J - Spec(R) is a normal space if and only if Max(R) is a retract of J - Spec(R) .A ring R is said to be NJ if J (R) = N (R) . This paper mainly studies the relationship between NJ rings and related rings, and investigates the Dorroh extension, the Nagata extension, the Jordan extension, and some other extensions of NJ rings. At the same time, we also prove that if R is a weakly 2-primal α -compatible ring with an isomorphism α of R , then R[x; α] is NJ; if R is a weakly 2-primal δ -compatible ring with a derivation δ of R , then R[x; δ] is NJ. Moreover, we consider some topological conditions for NJ rings and show for a NJ ring R that R is J-pm if and only if J - Spec(R) is a normal space if and only if Max(R) is a retract of J - Spec(R) .

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Bu Makaleye Atıf Yap

REN, Y., JIANG, M., WANG, Y. (2022). Extensions and topological conditions of NJ rings. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 44–62. https://ajindex.com/articles/608089

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