On the Commutativity of a Prime ∗-Ring with a ∗-α-Derivation

  • Gülay BOSNALI Çanakkale Onsekiz Mart University
  • Neşet AYDIN Çanakkale Onsekiz Mart University
  • Selin TÜRKMEN Çanakkale Onsekiz Mart University
Keywords: -derivation, --derivation, left -centralizer, 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.

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Published
2018-07-31
How to Cite
BOSNALI, G., AYDIN, N., & TÜRKMEN, S. (2018). On the Commutativity of a Prime ∗-Ring with a ∗-α-Derivation. JOURNAL OF SCIENTIFIC PERSPECTIVES, 2(3), 51-60. https://doi.org/10.26900/jsp.2018342244
Section
Basic Science and Engineering