Differential Identities in Rings and Algebras and their Applications
暫譯: 環與代數中的微分同一性及其應用

這本專著總結了在最近幾十年中顯著推進該領域的研究結果和方法。為了使這本專著儘可能自足，第一章提供了對該主題的簡要介紹。

Shakir Ali is a Professor of Mathematics at the Aligarh Muslim University (AMU), Aligarh, India. He received his Ph.D. degree in Mathematics (2002) from AMU. He also worked as an Associate Professor at King Abdulaziz University, Jeddah, Saudi Arabia during December 2014 to August 2018. He is president of the Joint Indian-Indonesian-Iran-Malaysia-Turkey (IIIMT)-Algebra Forum. He was awarded TUBITAK (Turkey) and ISM-University Malaya (Malaysia) visiting professorships for the years 2019-2022 and 2023-2024, respectively. He is an author and co-author of more than 150 publications in reputed international journals and has been on research visits to several universities and institutions across the word to deliver invited\plenary\keynote lectures. Besides supervising several students for M. Phil/Ph.D. degrees in various disciplines of Mathematics, namely, Ring theory, Module Theory, Coding theory and Cryptography, Professor S. Ali has successfully completed many national and international research projects awarded by the University Grants Commission (UGC), Department of Science and Technology (DST), India, DSR-KAU, Kingdom of Saudi Arabia, TUBITAK, Goverment of Turkey. Presently, he is Editor / Managing Editor of several reputed international mathematical journals. He is also a co-editor of several research volumes and a life member of the American Mathematical Society, Indian Mathematical Society, Calcutta Mathematical Society, the Indian Science Congress Association, the Indian Society of Industrial and Applied Mathematics, the Ramanujan Mathematical Society.

Mohammad Ashraf is a retired Professor and a Former Chairperson, Department of Mathematics, Aligarh Muslim University, Aligarh, India. He is also a Former Dean, Faculty of Science, Aligarh Muslim University. He has published more than 250 peer-reviewed scientific articles in Internationally recognized and reputed journals. He has organized several international conferences and has edited Eight research Proceedings / Volumes. Besides supervising one and half dozen of students for Ph.D. degrees in various disciplines of Mathematics namely Ring theory, Linear Algebra, Coding theory and Graph theory, Prof. Ashraf has successfully completed many national and international research projects awarded by the University Grants Commission, Department of Science and Technology and National Board of Higher Mathematics. Currently, he is Editor / Managing Editor of many reputed international Mathematical journals. He is also a life member of the Indian Mathematical Society, Calcutta Mathematical Society, the Indian Science Congress Association, and the Indian Society of Industrial and Applied Mathematics.

Vincenzo De Filippis is a Professor of Mathematics at the University of Messina, Italy. He received his Ph.D. degree in Mathematics (1999) from the University of Messina, Italy. He is an author and co-author of more than 100 publications in professional journals and has been on research visits to several Institutions in Europe and Asia. His research interests include Ring Theory, Theory of Associative Algebras, and Linear and Multilinear Algebras. His theoretical work is primarily aimed at studying the structure of algebras satisfying functional identities. He has delivered many invited and plenary lectures at International Conferences on algebraic structures and their applications. He is also a co-editor of various research volumes and a member of the Italian Mathematical Society (UMI) and the National Society of Algebraic and Geometric Structures and their Applications (GNSAGA-INDAM).

Lahcen Oukhtite is a Professor at the Department of Mathematics, Faculty of Science and Technology, University Sidi Mohamed Ben Abdellah Fez (USMBA), Morocco. He is also Director of the laboratory of modelling and mathematical structures (USMBA). He received his PhD degree in mathematics (in 2000) from USMBA. He is an author and coauthor of more than 110 articles published in reputed international mathematical journals. He supervised more than 16 PhD theses and his research interests include rings theory, commutativity and structure of rings and near-rings, derivations in rings and Banach algebras, central simple algebras with involution, semi- simple algebras, graph Theory. He has organized several International conferences and edited four volumes and conference proceedings. He had visited several foreign countries to deliver plenary and invited lectures at international conferences and seminars. Professor Oukhtite is also member of editorial board of many international mathematical journals.

Nadeem ur Rehman is a Professor in the Department of Mathematics at Aligarh Muslim University (AMU), India. After earning his Ph.D. from AMU in 2000, he was awarded a DAAD postdoctoral fellowship in Germany. His teaching career began at the Birla Institute of Science and Technology, Pilani, before joining AMU in 2006. He was promoted to Associate Professor in 2015 and Professor in 2018, with a two-year tenure at Taibah University, KSA, from 2015 to 2017. Dr. Rehman has supervised numerous scholars, including ten Ph.D. students in areas such as Ring Theory, Coding Theory, and Graph Theory. He has presented research at international conferences and was a Visiting Scientist at the University of Maribor, Slovenia, under a bilateral exchange. With support from agencies like the DST, CSIR, and UGC, he has led major research projects and is an active reviewer for publishers like Elsevier, Springer, and AMS. A life member of several mathematical societies, he continues to contribute significantly to teaching and research.

**Shakir Ali** 是印度阿里格爾穆斯林大學（AMU）數學系的教授。他於2002年在AMU獲得數學博士學位。2014年12月至2018年8月，他曾在沙烏地阿拉伯吉達的阿卜杜勒阿齊茲國王大學擔任副教授。他是印度-印尼-伊朗-馬來西亞-土耳其（IIIMT）代數論壇的主席。他曾獲得土耳其TUBITAK和馬來西亞馬來亞大學（ISM）於2019-2022年及2023-2024年的訪問教授職位。他是150多篇在知名國際期刊上發表的出版物的作者和合著者，並曾前往世界各地的多所大學和機構進行邀請演講、專題演講和主題演講。除了指導多位學生獲得數學各領域的碩士及博士學位（如環論、模論、編碼理論和密碼學）外，S. Ali教授還成功完成了多個由印度大學補助委員會（UGC）、印度科學技術部（DST）、沙烏地阿拉伯DSR-KAU和土耳其政府TUBITAK頒發的國內外研究項目。目前，他是多本知名國際數學期刊的編輯/主編。他也是多部研究專著的共同編輯，並且是美國數學學會、印度數學學會、加爾各答數學學會、印度科學大會、印度工業與應用數學學會及拉馬努金數學學會的終身會員。

**Mohammad Ashraf** 是印度阿里格爾穆斯林大學數學系的退休教授及前系主任。他也是阿里格爾穆斯林大學科學學院的前院長。**他在國際知名的期刊上發表了超過250篇經過同行評審的科學文章。**他組織了多場國際會議並編輯了八部研究論文集/專著。除了指導約18位學生獲得數學各領域的博士學位（如環論、線性代數、編碼理論和圖論）外，Ashraf教授還成功完成了多個由大學補助委員會、科學技術部及國家高等數學委員會頒發的國內外研究項目。目前，他是多本知名國際數學期刊的編輯/主編。他也是印度數學學會、加爾各答數學學會、印度科學大會及印度工業與應用數學學會的終身會員。

**Vincenzo De Filippis** 是意大利梅西納大學的數學教授。他於1999年在梅西納大學獲得數學博士學位。他是超過100篇在專業期刊上發表的出版物的作者和合著者，並曾前往歐洲和亞洲的多個機構進行研究訪問。他的研究興趣包括環論、聯合代數理論以及線性和多線性代數。他的理論工作主要旨在研究滿足函數性質的代數結構。他在國際會議上就代數結構及其應用發表了多場邀請和專題演講。他也是多部研究專著的共同編輯，並且是意大利數學學會（UMI）及代數和幾何結構及其應用國家學會（GNSAGA-INDAM）的成員。

**Lahcen Oukhtite** 是摩洛哥Sidi Mohamed Ben Abdellah大學（USMBA）科學與技術學院數學系的教授。他也是數學建模與結構實驗室的主任。他於2000年在USMBA獲得數學博士學位。他是超過110篇在知名國際數學期刊上發表的文章的作者和合著者。他指導了超過16篇博士論文，研究興趣包括環論、環和近環的可交換性及結構、環和巴拿赫代數中的導數、具有反演的中心簡單代數、半簡單代數及圖論。他組織了多場國際會議並編輯了四部專著和會議論文集。他曾前往多個國家在國際會議和研討會上發表專題和邀請演講。Oukhtite教授也是多本國際數學期刊的編輯委員會成員。

**Nadeem ur Rehman** 是印度阿里格爾穆斯林大學（AMU）數學系的教授。他於2000年在AMU獲得博士學位後，獲得德國DAAD的博士後獎學金。他的教學生涯始於比爾拉科學與技術學院（Birla Institute of Science and Technology），並於2006年加入AMU。他於2015年晉升為副教授，2018年晉升為教授，並於2015年至2017年在沙烏地阿拉伯的泰巴大學任教兩年。Rehman博士指導了多位學者，包括十位在環論、編碼理論和圖論等領域的博士生。他在國際會議上發表研究，並曾在斯洛維尼亞馬里博大學擔任訪問科學家，進行雙邊交流。在DST、CSIR和UGC等機構的支持下，他主導了多個重大研究項目，並且是Elsevier、Springer和AMS等出版商的活躍審稿人。他是多個數學學會的終身會員，並持續對教學和研究做出重要貢獻。