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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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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:
A Note on Monotone Bi-derivations On Lattices
Author(s):
Areej Almuhaimeed1, Faiza Shujat1, Abu Zaid Ansari2
1Department
of Mathematics,
College of Science,
Taibah University, Madinah,
Saudi Arabia.
E-mail:
aamuhaimeed@taibahu.edu.sa
fullahkhan@taibahu.edu.sa
2
Abstract:
The primary aim of this research is to delve deeply into the intriguing properties of symmetric bi-derivations on lattices, unveiling their complexities and potentials with unprecedented insight and clarity. Moreover, we characterize monotone bi-derivations and obtain some results in the context of the kernel of bi-derivations.
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.
Paper's Title:
Functional Identities of Additive Maps within Specialized Ring Structures
Author(s):
Abu Zaid Ansari
Department of Mathematics,
Faculty of Science,
Islamic University of Madinah,
Saudi Arabia.
E-mail: ansari.abuzaid@gmail.com
Abstract:
Let S be a (p+m)!-torsion-free semiprime ring, and
let B, k : S→S be additive mappings satisfying, for all y
∈ S, the identity
where γ and θ are automorphisms
of S. Then B is a generalized
(γ,θ)-derivation on B, with
k serving as its associated (γ,θ)-derivation. Moreover, analogously, we establish an additional result demonstrating that, if two additive mappings satisfy a prescribed identity, then each such mapping constitutes a generalized left
(γ,θ)-derivative having left
(γ,θ)-derivative. Furthermore, the appropriateness of this hypothesis is substantiated by explicit illustrative examples.
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