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## On $^*$-differential identities in prime rings with involution

#### Shakir ALİ  , Ali KOAM  , Moin ANSARİ 

Let $\mathcal{R}$ be a ring. An additive map $x\mapsto x^*$ of $\mathcal{R}$ into itself is called an involution if (i) $(xy)^*=y^*x^*$ and (ii) $(x^*)^*=x$ hold for all $x,y\in \mathcal{R}$. In this paper, we study the effect of involution $"*"$ on prime rings that satisfying certain differential identities. The identities considered in this manuscript are new and interesting. As the applications, many known theorems can be either generalized or deduced. In particular, a classical theorem due to Herstein [A note on derivation II, Canad. Math. Bull., 1979] is deduced.
prime ring, commutativity, involution, derivation, *-differential identities
•  S. Ali and H. Alhazmi, Some commutativity theorems in prime rings with involution and derivations, J. Adv. Math. Comput. Sci. 24 (5), 1–6, 2017.
•  S. Ali and N.A. Dar, On $*$-centralizing mappings in rings with involution, Georgian Math. J. 1, 25–28, 2014.
•  S. Ali and S. Huang, On derivations in semiprime rings, Algebr. Represent. Theory 15 (6), 1023–1033, 2012.
•  S. Ali, N.A. Dar, and M. Asci, On derivations and commutativity of prime rings with involution, Georgian Math. J. 23 (1), 9–14, 2016.
•  S. Ali, M.S. Khan, and M. Al-Shomrani, Generalization of Herstein theorem and its applications to range inclusion problems, J. Egyptian Math. Soc. 22, 322–326, 2014.
•  N. Argac, On prime and semiprime rings with derivations, Algebra Colloq. 13 (3), 371–380, 2006.
•  M. Ashraf and M.A. Siddeeque, On $*-$n-derivations in prime rings with involution, Georgian Math. J. 21 (1), 9–18, 2014.
•  M. Ashraf and N. Rehman, On commutativity of rings with derivations, Results Math. 42 (1-2), 3–8, 2002.
•  H.E. Bell, On the commutativity of prime rings with derivation, Quaest. Math. 22, 329-333, 1991.
•  H.E. Bell and M.N. Daif, On derivations and commutativity in prime rings, Acta Math. Hungar. 66, 337–343, 1995.
•  M.N. Daif, Commutativity results for semiprime rings with derivation, Int. J. Math. Math. Sci. 21 (3), 471–474, 1998.
•  N.A. Dar and S. Ali, On $*$-commuting mappings and derivations in rings with involution, Turk. J. Math. 40, 884–894, 2016.
•  V.De. Filippis, On derivation and commutativity in prime rings, Int. J. Math. Math. Sci. 69-72, 3859–3865, 2004.
•  A. Fosner and J. Vukman, Some results concerning additive mappings and derivations on semiprime rings, Pul. Math. Debrecen, 78 (3-4), 575–581, 2011.
•  I.N. Herstein, Rings with Involution, University of Chicago Press, Chicago, 1976.
•  I.N. Herstein, A note on derivation II, Canad. Math. Bull. 22, 509–511, 1979.
•  J. Mayne, Centralizing automorphisms of prime rings, Canad. Math. Bull. 19, 113– 117, 1976.
•  L. Oukhtite, Posner’s second theorem for Jordan ideals in ring with involution, Expo. Math. 4 (29), 415–419, 2011.
•  E.C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8, 1093–1100, 1957.
Birincil Dil en Matematik Matematik Orcid: 0000-0001-5162-7522Yazar: Shakir ALİ Kurum: Aligarh Muslim UniversityÜlke: India Orcid: 0000-0002-5047-9908Yazar: Ali KOAM Kurum: Jazan UniversityÜlke: Saudi Arabia Orcid: 0000-0002-1175-9704Yazar: Moin ANSARİ Kurum: Jazan UniversityÜlke: Saudi Arabia Yayımlanma Tarihi : 2 Nisan 2020
 Bibtex @araştırma makalesi { hujms588726, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2020}, volume = {49}, pages = {708 - 715}, doi = {10.15672/hujms.588726}, title = {On \$\^*\$-differential identities in prime rings with involution}, key = {cite}, author = {ALİ, Shakir and KOAM, Ali and ANSARİ, Moin} } APA ALİ, S , KOAM, A , ANSARİ, M . (2020). On $^*$-differential identities in prime rings with involution. Hacettepe Journal of Mathematics and Statistics , 49 (2) , 708-715 . DOI: 10.15672/hujms.588726 MLA ALİ, S , KOAM, A , ANSARİ, M . "On $^*$-differential identities in prime rings with involution". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 708-715 Chicago ALİ, S , KOAM, A , ANSARİ, M . "On $^*$-differential identities in prime rings with involution". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 708-715 RIS TY - JOUR T1 - On $^*$-differential identities in prime rings with involution AU - Shakir ALİ , Ali KOAM , Moin ANSARİ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.588726 DO - 10.15672/hujms.588726 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 708 EP - 715 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.588726 UR - https://doi.org/10.15672/hujms.588726 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics On $^*$-differential identities in prime rings with involution %A Shakir ALİ , Ali KOAM , Moin ANSARİ %T On $^*$-differential identities in prime rings with involution %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.588726 %U 10.15672/hujms.588726 ISNAD ALİ, Shakir , KOAM, Ali , ANSARİ, Moin . "On $^*$-differential identities in prime rings with involution". Hacettepe Journal of Mathematics and Statistics 49 / 2 (Nisan 2020): 708-715 . https://doi.org/10.15672/hujms.588726 AMA ALİ S , KOAM A , ANSARİ M . On $^*$-differential identities in prime rings with involution. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 708-715. Vancouver ALİ S , KOAM A , ANSARİ M . On $^*$-differential identities in prime rings with involution. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 715-708.

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