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

#### Shakir ALİ [1] , Ali KOAM [2] , Moin ANSARİ [3]

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
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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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