Maps Preserving Products and Derivations Advances in Algebraic Structures

Preface

1. Jordan Triple Homomorphisms on Selected Matrix Algebras

Introduction

Main Results

References

2. Characterization of Non-linear Mixed Jordan Triple *-derivations on*-algebras

Introduction

Main Result

Applications

References

3. Nonlinear Skew-Lie Triple Derivations on *-algebra

Introduction

Main Result

Applications

References

4. Fixed Product-Preserving Maps in Non-Associative Structures

Introduction

Preliminaries

Methodology

Main Results

Main Results

Conclusion

References

5. On Generalized (μ, η)-derivations in Semiprime Rings

Introduction

Generalized (μ, η)-derivation

Generalized Left (μ, η)-derivation

References

6. Fixed Product Preserving Mappings on Rings and Algebras

Introduction

Notation and Definitions

FPPMs on Matrices Over a Field

FPPMs for Alternative Division Rings (and Cayley-Dickson Algebras)

Fixed Product Preserving Mappings for Lie and Jordan Products

FPPMs on Algebras of Bounded Linear Operators

Bilinear Mappings with the Fixed Product Preserving Property for Invertible Elements

Applications

Some Open Questions

References

7. Maps Preserving n-tuple Product A*B + BA* on von Neumann Algebras

Introduction

Main Results

References

8. Nonlinear n-tuple *-Jordan Derivations on von Neumann Algebras

Introduction

Main Results

References

9. Non-linear n-tuple A*B + BA*Derivations on*-algebras

Introduction

Main Results

References

10. Note on Mixed Skew Product on Factor von Neumann Algebras

Brief Historical Development and Motivation

Additivity of Mapping Φ

Isomorphism of the Mapping Φ

References 168

11. On Centrally Extended Generalized Jordan *-derivations and Related Maps in Rings

Introduction

Preliminary Results

Results on Centrally Extended Generalized Jordan *-derivations

References

12. On Commutativity of ∇-prime Rings with Derivations

Introduction

Preliminary Results

Main Results

References

13. Lie Higher Derivations of Arbitrary Triangular Algebras

Introduction

Preliminaries

Lie Higher Derivations of Arbitrary Triangular Algebras

Topics for Further Research

References

Index

Biography

Dr. Vahid Darvish is an Associate Professor at the Nanjing University of Information Science and Technology (NUIST) in Nanjing, China. He obtained a PhD in Mathematics in 2016 from the University of Mazandaran, where he was recognized as the top graduate student by the National Elites Foundation (NEF) of Iran. Supported by NEF, he conducted two years of postdoctoral research and served as a lecturer and researcher at the University of Mazandaran. He was a research fellow at Victoria University in Melbourne, Australia.

Dr. Darvish’s research focuses primarily on maps preserving problems, an area in which he has published numerous high-impact papers in prestigious international journals. He undertook a one-year project at the University of Applied Sciences Upper Austria in 2018 and an internship at Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil in 2019. He was also selected for the Talented Young Scientist Program, supported by the Ministry of Science and Technology of China, by which he started his career at NUIST. As an active member of the global academic community, Dr. Darvish serves as a reviewer for a wide variety of journals such as Mathematical Reviews and Zentralblatt MATH.

Dr. Nadeem ur Rehman is a Professor of Mathematics at Aligarh Muslim University, India. He earned his Ph.D. from AMU in 2000 and later held a DAAD postdoctoral fellowship in Germany. He began his career at BITS Pilani before rejoining AMU in 2006, where he became an Associate Professor in 2015 and a Professor in 2018. He also served as an Associate Professor at Taibah University, Saudi Arabia (2015–2017).

Dr. Rehman has published over 200 research papers in reputed international journals and has supervised 11 Ph.D. and 3 M.Phil. scholars, with five Ph.D. students currently under his guidance in Ring Theory, Coding Theory, and Graph Theory. He has presented his work worldwide and was a Visiting Scientist at the University of Maribor, Slovenia, under an Indo-Slovenian DST–MHEST program and TUBITAK Visiting Professor/Scientist at the Karamanoglu Mehmetbey University, Karaman, Turkey.

He has completed several major research projects funded by UGC, DST, NBHM, and CSIR, and is a life member of leading Indian mathematical societies. He also serves as a reviewer for major publishers, including Elsevier, Springer, Taylor & Francis, AMS, and Zentralblatt Math.

Dr. Mohd Arif Raza is an Associate Professor of Mathematics at the Faculty of Sciences and Arts-Rabigh, King Abdulaziz University in Jeddah, Saudi Arabia. He got his PhD in mathematics from Aligarh Muslim University in 2015, and his thesis entitled “Differential Identities in Rings and Algebras" demonstrated his significant analytical ability and novel approach to mathematical research. His academic career has been defined by several significant responsibilities, including the Assistant Professor post at King Abdulaziz University in Jeddah and Galgotias University in India. Dr. Raza's research interests are extensive and diverse, including associative and non-associative algebras, differential identities, coding theory, graph theory, and other areas of the theory of rings and algebras. His contributions to the subject are significant, with 64 research papers published in high-impact peer-reviewed publications and several chapters in scholarly books. He has given an “invited talk’ and presented his work at several national and international conferences. Dr. Raza, a proactive academic, serves as both a mentor and a researcher, supervising master's theses and leading funded research projects sponsored by King Abdulaziz University's Deanship of Scientific Research and the Saudi Ministry of Education. His scientific activities are supplemented by his work as a reviewer for famous journals, which demonstrates his dedication to the promotion of mathematical sciences.

Dr. Junaid Nisar is an Assistant Professor at Symbiosis International University, Symbiosis Institute of Technology, Pune, India. He obtained a PhD in 2023 from Aligarh Muslim University, India, and is well-regarded for his expertise in both research and academics. Dr. Nisar has an impressive publication record in reputable SCI-indexed journals. In addition to his academic accomplishments, Dr. Nisar has qualified for national-level exams, securing the CSIR-NET Junior Research Fellowship (JRF) in 2017 and 2018, and passing the GATE exam in 2022. His research focuses primarily on mapping-preserving problems within various algebraic structures and rings, contributing valuable insights to the field. Dr. Nisar is an active member of the global research community, serving as a reviewer for several SCI-indexed journals.