http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Some results on centralizers of semiprime rings
Abu Zaid Ansari 한국전산응용수학회 2022 Journal of Applied and Pure Mathematics Vol.4 No.3
The objective of this research paper is to prove that an additive mapping T from a semiprime ring R to itself will be centralizer having a suitable torsion restriction on R if it satisfy any one of the following algebraic equations \begin{enumerate} \item [$(a)$] $2T(x^{n}y^{n}x^{n})=T(x^{n})y^{n}x^{n}+x^{n}y^{n}T(x^{n})$ \item [$(b)$] $3T(x^{n}y^{n}x^{n})=T(x^{n})y^{n}x^{n}+x^{n}T(y^{n})x^{n}+x^{n}y^{n}T(x^{n})$ \mbox{~for~every~}$x, y\in R$. \end{enumerate} Further, few extensions of these results are also presented in the framework of \ast-ring.
SOME RESULTS ON CENTRALIZERS OF SEMIPRIME RINGS
ANSARI, ABU ZAID The Korean Society for Computational and Applied M 2022 Journal of applied and pure mathematics Vol.4 No.3/4
The objective of this research paper is to prove that an additive mapping T from a semiprime ring R to itself will be centralizer having a suitable torsion restriction on R if it satisfy any one of the following algebraic equations (a) 2T(x<sup>n</sup>y<sup>n</sup>x<sup>n</sup>) = T(x<sup>n</sup>)y<sup>n</sup>x<sup>n</sup> + x<sup>n</sup>y<sup>n</sup>T(x<sup>n</sup>) (b) 3T(x<sup>n</sup>y<sup>n</sup>x<sup>n</sup>) = T(x<sup>n</sup>)y<sup>n</sup>x<sup>n</sup>+x<sup>n</sup>T(y<sup>n</sup>)x<sup>n</sup>+x<sup>n</sup>y<sup>n</sup>T(x<sup>n</sup>) for every x, y ∈ R. Further, few extensions of these results are also presented in the framework of *-ring.
Semiprime rings with involution and centralizers
Abu Zaid Ansari,Faiza Shujat 한국전산응용수학회 2022 Journal of applied mathematics & informatics Vol.40 No.3
The objective of this research is to prove that an additive mapping T:R\to R is a left as well as right centralizer on R if it satisfies any one of the following identities: \begin{enumerate} \item [$(i)$] $T(x^{n}y^{n}+y^{n}x^{n})=T(x^n)y^{n}+y^nT(x^{n})$ \item [$(ii)$] $2T(x^{n}y^{n})=T(x^n)y^{n}+y^nT(x^{n})$ \end{enumerate} for each x,y\in R, where n\geq 1 is a fixed integer and $R$ is any n!-torsion free semiprime ring. In addition, we talk over above identities in the setting of \ast-ring(ring with involution).
Endomorphisms, anti-endomorphisms and bi-semiderivations on rings
Abu Zaid Ansari,Faiza Shujat,Ahlam Fallatah 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.1
The goal of this study is to bring out the following conclusion: Let $\mathcal{R}$ be a non-commutative prime ring of characteristic not two and $\mathcal{D}$ be a bi-semiderivation on $\mathcal{R}$ with a function $\mathfrak{f}$ (surjective). If $\mathcal{D}$ acts as an endomorphism or as an anti-endomorphism, then $\mathcal{D} =0$ on $\mathcal{R}$.