Yıl 2020, Cilt 49 , Sayı 2, Sayfalar 578 - 585 2020-04-02

On centrally-extended multiplicative (generalized)-$(\alpha,\beta)$-derivations in semiprime rings

Najat MUTHANA [1] , Zakeiah ALKHAMİSİ [2]


Let $R$ be a ring with center $Z$ and $\alpha$, $\beta$ and $d$ mappings of $R$. A mapping $F$ of $R$ is called a centrally-extended multiplicative (generalized)-$(\alpha,\beta)$-derivation associated with $d$ if $F(xy)-F(x)\alpha(y)-\beta(x)d(y)\in Z$ for all $x, y \in R$. The objective of the present paper is to study the following conditions: (i) $F(xy)\pm \beta(x)G(y)\in Z$, (ii) $F(xy)\pm g(x)\alpha(y)\in Z$ and (iii) $F(xy)\pm g(y)\alpha(x)\in Z$ for all $x,y$ in some appropriate subsets of $R$, where $G$ is a multiplicative $($generalized$)$-$(\alpha,\beta)$-derivation of $R$ associated with the map $g$ on $R$.
Semiprime ring, left ideal, multiplicative (generalized)-derivation, multiplicative (generalized)-$(\alpha;\beta)$-derivation, centrally-extended generalized $(\alpha;\beta)$-derivation, centrally-extended multiplicative (generalized)-$(\alpha;\beta)$-derivation, generalized $(\alpha;\beta)$-derivation
  • [1] A. Ali, B. Dhara, S. Khan and F. Ali, Multiplicative (generalized)-derivations and left ideals in semiprime rings, Hacettepe J. Math. Stat. 44 (6), 1293–1306, 2015.
  • [2] H.E. Bell and M.N. Daif, On centrally-extended maps on rings, Beitrage Algebra Geom. Article No. 244, 1–8, 2015.
  • [3] B. Dhara and S. Ali, On multiplicative (generalized)-derivations in prime and semiprime rings, Aequat. Math. 86 (1-2), 65–79, 2013.
  • [4] C. Lanski, An Engel condition with derivation for left ideals, Proc. Amer. Math. Soc. 125 (2), 339–345, 1997.
  • [5] M.S. Tammam El-Sayiad, N.M. Muthana and Z.S. Alkhamisi, On rings with some kinds of centrally-extended maps, Beitr¨age Algebra Geom. Article No. 274, 1–10, 2015.
Birincil Dil en
Konular Matematik
Bölüm Matematik
Yazarlar

Orcid: 0000-0001-9929-2776
Yazar: Najat MUTHANA
Kurum: University of Jeddah
Ülke: Saudi Arabia


Orcid: 0000-0001-8140-5015
Yazar: Zakeiah ALKHAMİSİ (Sorumlu Yazar)
Kurum: King Abdulaziz University
Ülke: Saudi Arabia


Tarihler

Yayımlanma Tarihi : 2 Nisan 2020

Bibtex @araştırma makalesi { hujms568378, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2020}, volume = {49}, pages = {578 - 585}, doi = {10.15672/hujms.568378}, title = {On centrally-extended multiplicative (generalized)-\$(\\alpha,\\beta)\$-derivations in semiprime rings}, key = {cite}, author = {MUTHANA, Najat and ALKHAMİSİ, Zakeiah} }
APA MUTHANA, N , ALKHAMİSİ, Z . (2020). On centrally-extended multiplicative (generalized)-$(\alpha,\beta)$-derivations in semiprime rings. Hacettepe Journal of Mathematics and Statistics , 49 (2) , 578-585 . DOI: 10.15672/hujms.568378
MLA MUTHANA, N , ALKHAMİSİ, Z . "On centrally-extended multiplicative (generalized)-$(\alpha,\beta)$-derivations in semiprime rings". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 578-585 <https://dergipark.org.tr/tr/pub/hujms/issue/53568/568378>
Chicago MUTHANA, N , ALKHAMİSİ, Z . "On centrally-extended multiplicative (generalized)-$(\alpha,\beta)$-derivations in semiprime rings". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 578-585
RIS TY - JOUR T1 - On centrally-extended multiplicative (generalized)-$(\alpha,\beta)$-derivations in semiprime rings AU - Najat MUTHANA , Zakeiah ALKHAMİSİ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.568378 DO - 10.15672/hujms.568378 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 578 EP - 585 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.568378 UR - https://doi.org/10.15672/hujms.568378 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On centrally-extended multiplicative (generalized)-$(\alpha,\beta)$-derivations in semiprime rings %A Najat MUTHANA , Zakeiah ALKHAMİSİ %T On centrally-extended multiplicative (generalized)-$(\alpha,\beta)$-derivations in semiprime rings %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.568378 %U 10.15672/hujms.568378
ISNAD MUTHANA, Najat , ALKHAMİSİ, Zakeiah . "On centrally-extended multiplicative (generalized)-$(\alpha,\beta)$-derivations in semiprime rings". Hacettepe Journal of Mathematics and Statistics 49 / 2 (Nisan 2020): 578-585 . https://doi.org/10.15672/hujms.568378
AMA MUTHANA N , ALKHAMİSİ Z . On centrally-extended multiplicative (generalized)-$(\alpha,\beta)$-derivations in semiprime rings. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 578-585.
Vancouver MUTHANA N , ALKHAMİSİ Z . On centrally-extended multiplicative (generalized)-$(\alpha,\beta)$-derivations in semiprime rings. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 585-578.