Paper's Title:

Additive Mappings on Semiprime Rings Functioning as Centralizers

Author(s):

Abu Zaid Ansari and Faiza Shujat

Department of Mathematics,
Faculty of Science,
Islamic University of Madinah, Madinah
K.S.A.
E-mail: ansari.abuzaid@gmail.com, ansari.abuzaid@iu.edu.sa

Department of Mathematics,
Faculty of Science,
Taibah University, Madinah,
K.S.A.
E-mail: faiza.shujat@gmail.com, fullahkhan@taibahu.edu.sa

Abstract:

The objective of this research is to prove that an additive mapping T:R → R is a centralizer on R if it satisfies any one of the following identities:

for all x ∈ R, where n ≥ 1 is a fixed integer and R is any suitably torsion free semiprime ring. Some results on involution "*" are also presented as consequences of the main theorems. In addition, we will take criticism in account with examples.

Paper's Title:

On Automorphisms and Bi-derivations of Semiprime Rings

Author(s):

Abu Zaid Ansari, Faiza Shujat, Ahlam Fallatah

Department of Mathematics,
Faculty of Science,
Islamic University of Madinah, Madinah
K.S.A.
E-mail: ansari.abuzaid@gmail.com, ansari.abuzaid@iu.edu.sa

Department of Mathematics
Faculty of Science
Taibah University, Madinah,
K.S.A.
E-mail: faiza.shujat@gmail.com, fullahkhan@taibahu.edu.sa

Department of Mathematics
Faculty of Science
Taibah University, Madinah,
K.S.A.
E-mail: Afallatah@taibahu.edu.sa
 

Abstract:

In this article, our goal is to figure out a functional equation involving automorphisms and bi-derivations on certain semiprime ring. Also, we characterize the structure of automorphism, in case of prime rings.

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