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Yapay Zeka Hızlı Bakış & Çıkarımlar
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As a consequence, we show that the semiprimeness (semisimpleness) of the ring (M, +, ·γ) for any γ ∈ Γ implies the Γsemiprimeness(Γ-semisimpleness) of the Γ-ring M.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Let M be a weak Nobusawa Γ-ring and γ be a nonzero element of Γ.
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Temel Bulgular & Veri:In this paper, we find a relation between Γ-rings and rings, and give some commutativity conditions on Γ-rings by using this relation.
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Sonuç & Katkı:As a consequence, we show that the semiprimeness (semisimpleness) of the ring (M, +, ·γ) for any γ ∈ Γ implies the Γsemiprimeness(Γ-semisimpleness) of the Γ-ring M.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:gamma ring · prime Γ-ring · k-derivation
Abstract
Let M be a weak Nobusawa Γ-ring and γ be a nonzero element of Γ. In this paper, we find a relation between Γ-rings and rings, and give some commutativity conditions on Γ-rings by using this relation. Also, we prove that any Γ-ring M in the sense of Nobusawa with a nonzero element γ in the center of M-ring Γ is γ-prime if and only if M is Γ-prime. As a consequence, we show that the semiprimeness (semisimpleness) of the ring (M, +, ·γ) for any γ ∈ Γ implies the Γsemiprimeness(Γ-semisimpleness) of the Γ-ring M.
Anahtar kelimeler
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Bu Makaleye Atıf Yap
Arslan, O., Kandamar, H. (2016). On commutativity of prime gamma rings with derivation. Hacettepe Journal of Mathematics and Statistics, Volume: 45 Issue: 5. https://ajindex.com/articles/1403090