• Chennupalle Divya
• Shaik Haseena
• C. Jaya Subba Reddy

Let R be a semiprime ring with center Z, S be a non-empty subset of R, α be an endomorphism on R and d be an (α,1) reverse derivation of R. A mapping d:R→R is called centralizing derivation of S if [d(x),x]∈Z, for all x∈S. In the present paper, we study some centralizing properties of (α,1) Reverse derivations in semiprime rings one of the following conditions holds: (i)d([x,y])=〖[x,y]〗_(α,1) , for all x, y ∈ R. (ii)d([x,y])= 〖-[x,y]〗_(α,1) , for all x, y ∈ R. (iii)d(x)d(y)∓xy∈Z, for all x, y ∈ R. (iv)d(xoy)=〖(xoy)〗_(α,1) , for all x, y ∈ R. (v)d(xoy)= -〖(xoy)〗_(α,1) , for all x, y ∈ R. Also we prove that d is centralizing on R if d acts as a homomorphism on R and d is centralizing on S if d acts as an anti-homomorphism on R.

Semiprime ring, Reverse derivation, (α,1)- Reverse derivation, Centralizing mappings, homomorphism and anti-homomorphism

"CENTRALIZING PROPERTIES OF (α, 1)- REVERSE DERIVATIONS IN SEMIPRIME RINGS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.8, Issue 12, page no.c45-c50, December-2021, Available :http://www.jetir.org/papers/JETIR2112207.pdf

"CENTRALIZING PROPERTIES OF (α, 1)- REVERSE DERIVATIONS IN SEMIPRIME RINGS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.8, Issue 12, page no. ppc45-c50, December-2021, Available at : http://www.jetir.org/papers/JETIR2112207.pdf