Maps Preserving Products and Derivations

The volume explores the preservation properties of maps within complex algebraic structures. It comprises two parts. The first section focuses on the analysis of maps that preserve products within various algebraic frameworks, including semiprime rings, matrix algebras, and von Neumann algebras. It examines the conditions under which these maps maintain product structures, providing insights into their behaviour and implications in different algebraic settings. The discussions extend to the exploration of specific cases where these preservation properties are crucial, offering a detailed examination of how product-preserving maps influence the structural integrity of diverse algebraic entities. The second section shifts attention to the study of maps that preserve derivations, which play a critical role in the study of algebraic structures and their transformations. This part explores various forms of derivations and the maps that preserve them, highlighting their impact on the underlying algebraic structures. It delves into both linear and nonlinear contexts, examining how these maps affect the properties and behaviour of rings and algebras, offering valuable insights into the algebraic theory of derivations. The volume is a comprehensive resource for researchers and practitioners interested in the preservation properties of algebraic maps, contributing to advancing knowledge in the field of algebraic structures and their symmetries.

Key Features:

• Explores advanced concepts in algebraic structures
• Covers both product and derivation preservation
• Comprehensive coverage of both additive and linear maps
• Provides valuable theoretical and practical insights
• Essential resource for advanced researchers.

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.