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

Yıl 2018, Cilt: 2 Sayı: 3, 51 - 60, 31.07.2018

Öz

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. 

Kaynakça

  • References [1] HERSTEIN I.N., 1976, Rings with Involutions, Chicago Univ., Chicago Press. [2] KIM K. H. and LEE Y. H., 2017, A Note on ∗-Derivation of Prime ∗-Rings, International Mathematical Forum, 12(8), 391-398. [3] REHMAN N., ANSARI A. Z. and HAETINGER C., 2013, A Note on Homomorphisims and Anti- Homomorphisims on ∗-Ring, Thai Journal of Mathematics, 11(3), 741-750. [4] POSNER E.C.,1957, Derivations in Prime Rings, Proc. Amer. Math. Soc., 8:1093-1100. [5] BRESAR M. and VUKMAN J.,1989, On Some Additive Mappings in Rings with Involution, Aequationes Math., 38, 178-185. 10 Gu¨lay BOSNALI et al. [6] HERSTEIN I.N.,1957, Jordan Derivations of Prime Rings, Proc. Amer. Math. Soc., 8(6), 11041110. [7] ZALAR B., 1991, On Centralizers of Semiprime Rings, Comment. Math. Univ. Caroline, 32(4), 609-614. [8] SALHI A. and FOSNER A., 2010, On Jordan (α,β)∗-Derivations In Semiprime Rings, Int J. Algebra, 4(3), 99-108 [9] KOC¸ E., G¨OLBASI ¨O., 2017, Results On α-∗-Centralizers of Prime and Semiprime Rings with Involution, commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 66(1), 172-178.
Yıl 2018, Cilt: 2 Sayı: 3, 51 - 60, 31.07.2018

Öz

Kaynakça

  • References [1] HERSTEIN I.N., 1976, Rings with Involutions, Chicago Univ., Chicago Press. [2] KIM K. H. and LEE Y. H., 2017, A Note on ∗-Derivation of Prime ∗-Rings, International Mathematical Forum, 12(8), 391-398. [3] REHMAN N., ANSARI A. Z. and HAETINGER C., 2013, A Note on Homomorphisims and Anti- Homomorphisims on ∗-Ring, Thai Journal of Mathematics, 11(3), 741-750. [4] POSNER E.C.,1957, Derivations in Prime Rings, Proc. Amer. Math. Soc., 8:1093-1100. [5] BRESAR M. and VUKMAN J.,1989, On Some Additive Mappings in Rings with Involution, Aequationes Math., 38, 178-185. 10 Gu¨lay BOSNALI et al. [6] HERSTEIN I.N.,1957, Jordan Derivations of Prime Rings, Proc. Amer. Math. Soc., 8(6), 11041110. [7] ZALAR B., 1991, On Centralizers of Semiprime Rings, Comment. Math. Univ. Caroline, 32(4), 609-614. [8] SALHI A. and FOSNER A., 2010, On Jordan (α,β)∗-Derivations In Semiprime Rings, Int J. Algebra, 4(3), 99-108 [9] KOC¸ E., G¨OLBASI ¨O., 2017, Results On α-∗-Centralizers of Prime and Semiprime Rings with Involution, commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 66(1), 172-178.
Toplam 1 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Basic Sciences and Engineering
Yazarlar

Gülay Bosnalı Bu kişi benim

Neşet Aydın

Selin Türkmen Bu kişi benim

Yayımlanma Tarihi 31 Temmuz 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 2 Sayı: 3

Kaynak Göster

APA Bosnalı, G., Aydın, N., & Türkmen, S. (2018). On the Commutativity of a Prime ∗-Ring with a ∗-α-Derivation. Journal of Scientific Perspectives, 2(3), 51-60.