The aim of this paper is to prove the commutativity of a ∗-ring R with the followings conditions: i) if T is a homomorphism (or an antihomomorphism) on R,ii) if d([x,y]) = 0 for all x,y ∈ R, iii) if [d(x),y] = [α(x),y] for all x,y ∈ R, iv) if d(x)◦y = 0 for all x,y ∈ R, v) if d(x◦y) = 0 for all x,y ∈ R.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Let R be a prime ∗-ring where ∗ be an involution of R, α be an automorphism of R, T be a nonzero left α-∗-centralizer on R and d be a nonzero ∗-α-derivation on R.
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Temel Bulgular & Veri:Let R be a prime ∗-ring where ∗ be an involution of R, α be an automorphism of R, T be a nonzero left α-∗-centralizer on R and d be a nonzero ∗-α-derivation on R.
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Sonuç & Katkı:The aim of this paper is to prove the commutativity of a ∗-ring R with the followings conditions: i) if T is a homomorphism (or an antihomomorphism) on R,ii) if d([x,y]) = 0 for all x,y ∈ R, iii) if [d(x),y] = [α(x),y] for all x,y ∈ R, iv) if d(x)◦y = 0 for all x,y ∈ R, v) if d(x◦y) = 0 for all x,y ∈ R.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:∗-derivation · ∗-α-derivation · left ∗-centralizer
Abstract
Let R be a prime ∗-ring where ∗ be an involution of R, α be an automorphism of R, T be a nonzero left α-∗-centralizer on R and d be a nonzero ∗-α-derivation on R. The aim of this paper is to prove the commutativity of a ∗-ring R with the followings conditions: i) if T is a homomorphism (or an antihomomorphism) on R,ii) if d([x,y]) = 0 for all x,y ∈ R, iii) if [d(x),y] = [α(x),y] for all x,y ∈ R, iv) if d(x)◦y = 0 for all x,y ∈ R, v) if d(x◦y) = 0 for all x,y ∈ R.
BOSNALI, G., AYDIN, N., TÜRKMEN, S. (2018). On the Commutativity of a Prime ∗-Ring with a ∗-α-Derivation. Health Sciences Quarterly, Cilt: 2 - Sayı: 3, 51–60. https://ajindex.com/articles/836660
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