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Advances in Ring Theory and Applications: WARA22, Messina, Italy, July 18–20, 2022 de Shakir Ali

Advances in Ring Theory and Applications: WARA22, Messina, Italy, July 18–20, 2022: Springer Proceedings in Mathematics & Statistics, cartea 443

Editat de Shakir Ali, Mohammad Ashraf, Vincenzo De Filippis, Nadeem ur Rehman
en Limba Engleză Hardback – 29 apr 2024

Analiza derivărilor multiplicative și a idealelor în inele semiprime reprezintă unul dintre punctele de plecare ale acestui volum colectiv, care sintetizează progresele recente dintr-un domeniu fundamental al algebrei. Advances in Ring Theory and Applications documentează lucrările prezentate la workshop-ul WARA22 din Messina, oferind o perspectivă tehnică asupra stadiului actual al teoriei structurilor Lie și Jordan. Găsim în această carte o explorare riguroasă a hărților aditive, a automorfismelor și a comportamentului derivărilor în algebre asociative, teme care definesc cercetarea contemporană în algebra necomutativă.

Structura volumului reflectă o progresie de la identități centrale și derivări skew către aplicații în teoria grafurilor, cum este analiza indicilor topologici peste graful divizorilor lui zero. Credem că valoarea acestui text rezidă în capacitatea de a unifica ramuri aparent distincte, precum teoria grupurilor și algebra matricială, sub umbrela teoriei inelelor. Comparabil cu Algebra and Its Applications în rigurozitate, volumul de față este actualizat pentru noile dezvoltări din domeniul identităților funcționale și al structurilor cu involuție apărute după 2016.

În contextul operei editorilor, acest volum continuă direcția stabilită de Shakir Ali în Differential Identities in Rings and Algebras and their Applications, dar extinde cadrul de cercetare către aplicații practice în teoria grafurilor și reprezentări de grupuri simetrice. Este o lucrare de referință care nu doar prezintă rezultate, ci stabilește noi direcții de investigație pentru specialiștii în algebră abstractă.

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Specificații

ISBN-13: 9783031507946
ISBN-10: 3031507940
Pagini: 398
Ilustrații: XI, 398 p. 3 illus.
Dimensiuni: 155 x 235 mm
Greutate: 0.84 kg
Ediția:2024
Editura: Springer Nature Switzerland
Colecția Springer
Seria Springer Proceedings in Mathematics & Statistics

Locul publicării:Cham, Switzerland

De ce să citești această carte

Această lucrare este esențială pentru cercetătorii și doctoranzii în matematică care doresc să stăpânească ultimele tehnici din teoria inelelor asociative. Cititorul câștigă acces la demonstrații recente privind derivările generalizate și identitățile Lie, beneficiind de expertiza unor academicieni de talie mondială. Este un instrument indispensabil pentru înțelegerea modului în care structurile algebrice moderne interacționează cu teoria grafurilor și algebra computațională.

Despre autor

Editorii volumului, printre care se numără Shakir Ali și Mohammad Ashraf, sunt figuri proeminente în comunitatea matematică internațională, cu o activitate susținută în cadrul Aligarh Muslim University. Mohammad Ashraf are o experiență vastă în organizarea conferințelor de algebră, editând volume de referință în seria Springer Proceedings in Mathematics & Statistics. Shakir Ali este recunoscut pentru contribuțiile sale fundamentale în teoria identităților diferențiale. Împreună cu Vincenzo De Filippis și Nadeem ur Rehman, aceștia au curatoriat o selecție de lucrări care reflectă standardele academice înalte ale workshop-ului WARA22.

Cuprins

G. S. Sandhu, B. Dhara, S. Ghosh , A note on multiplicative (generalized)-derivations and left sided ideals in semiprime rings.- Nirbhay Kumar, Avanish Kumar Chaturved, On weekly generalized reversible rings.- Sk Aziz, Om Prakash, Additivity of multiplicative b-generalized (skew) derivations.- M. O. Alshammari, F. Ali, Specht Modules and Representations of Symmetric Group.- B. Dhara, S. Kar, K. Singh, Commutativity Theorems on Prime Rings with Generalized Derivations.- A. Abbasi, M. R. Mozumder, Commutativity of σ-prime rings with generalized derivation.- M. S. Pandey, A. Pandey, A note on b-generalized skew derivations on prime rings.- N. ur Rehman, S. A. Mir, M. Nazim, Analysis of some topological indices over the weakly zero-divisor graph of the ring Zp × Zq × Zr.- Md Arshad Madni, M. S. Akhtar, M. R. Mozumder, A study of central identities equipped with skew Lie product involving generalized derivations.- M. R. Mozumder, N. Parveen, W. Ahmed, Some results on left-sided ideals of semiprime rings with Symmetric (α, β) n-derivations.- A. Ali, K. Kumar, M. Tasleem, Central power values of generalized derivation and structure of unital Banach algebra.- A. Pandey, B. Prajapati, Generalized skew derivations of order 2 in prime rings with multilinear polynomials.- Zhi-Cheng Deng, F. Wei, Local and 2-local Lie-type Derivations of Operator Algebras on Banach Spaces.- F. Wei, Jing-Xiong Xu, The Noncommutative Singer-Wermer Conjecture and Generalized Skew Derivations.- M. Ashraf, M. A. Ansari, Md Shamim Akhter, Non-global multiplicative Lie triple derivations on rings.- A. Z. Ansari, F. Shujat, Algebraic identities on prime and semiprime rings.- G. Scudo, Generalized derivations with periodic values on prime rings.- L. Carini, V. De Filippis, On a functional identity involving power values of generalized skew derivations on Lie ideals.-  M. Andaloro, Generalized Skew Derivations with periodic values on Lie ideals.- M. Bera, B. Dhara, Generalized skew-derivations actingon multilinear polynomials in prime rings.- M. Salahuddin Khan, S. Ali, A. Nadim Khan, M. Ayedh, Results on b-generalized derivations in rings.- F. Shujat, A. Z. Ansari, Results on generalized skew bi-semiderivation in prime rings.- F. Ammendolia, Commuting iterates of generalized derivations on Lie ideals.- M. A. Raza, T. Al-Sobhi, Non-linear mappings preserving product m ∗n + n ∗m on factor von Neumann algebras.- F. Rania, A commutativity condition for semiprime rings with generalized skew derivations.- Faez A. Alqarni, Nadeem ur Rehman, Hafedh M. Alnoghashi, Results on Generalized Derivations in Prime Rings with Involution.- M. Ashraf, N. Khan, W. Rehman, G. Mohammad, Quantum codes over an extension of Z4.- N. Parveen, Product of Traces of Permuting n-Derivations on Prime and Semiprime Ideals of a Ring.

Notă biografică

Dr. Shakir Ali is an Associate Professor, Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, India. He is also worked as an Associate Professor, Faculty of Science, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia during 2014 -2018. He has published more than 120 peer-reviewed scientific articles in Internationally recognized and reputed journals with more than 3300 citations, 29 h-index, and 76 i10-index according to Google Scholar. Dr. Ali is the recipient of TUBITAK Visiting Professor/Scientists fellowship awards for the year 2019 and 2022, sponsored by The Scientific and Technological Research Council of Turkey, Government of Turkey. In 2011, he (jointly with Professors M. Ashraf and N. Rehman) has received Indo-Slovenian Inter-Governmental Exchange Research Programme of cooperation in Science and Technology under the auspices of the Ministry of Science and Technology (DST), India and Ministry of Higher Education Science and Technology (MHEST), Republic of Slovenia.  Dr. Ali has been given the Outstanding Scientist Award for the Years 2018 by IOSRD. Moreover, he awarded the ‘Best Research Paper Award in Algebra’ for the years 2003 and 2008 by the Indian Mathematical Society (IMS) at its 69th & 74th annual conferences.  He has supervised five Ph.D. and M. Phil. dissertations on the theory of derivations in associative rings and algebras. He has attended more than 80 conferences and delivered about 60 invited talks and 19 presentations at various universities and institutions across the globe. He has completed many national and international major research projects from DSR-KAU (Kingdom of Saudi Arabia), SERB-DST, UGC(India) and TUBITAK (Turkey). Currently, Dr. Ali  is Editor/Deputy Managing Editor of several reputed national and international mathematical journals. Dr. Ali is a life member of the Indian Mathematical Society(IMS), Mathematical Teachers Association (MTA), Ramanujam Mathematical Society(RMS), Indian Science Congress Association(ISCA) and Calcutta Mathematical Society(CMS). He has also been a member of the American Mathematical Society (AMS), since 2014 and a member of the Asian Council of Science Editors(ACSE), since January 2016. Dr. Ali is also a reviewer of the AMS Mathematical Reviews and is a referee of several mathematics journals.

Mohammad Ashraf is Professor and Chairperson, Department of Mathematics, Aligarh Muslim University, Aligarh, India. He  has also served  in the capacity of the  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  Five research Proceedings/volumes.  After completing a Ph.D. from Aligarh Muslim University in 1986, he started his teaching carrier as a Lecturer in the Department of Mathematics, Aligarh Muslim University, Aligarh. He was awarded the Young Scientist Award by the Indian Science Congress Association in the year 1988 for his work on Power maps in Rings and subsequently awarded I.M.S. Prize by the  Indian Mathematical Society  in the year 1995. He was elevated to the post of Reader in 1997, and finally became Professor of Mathematics in 2005.  He has also served as Associate Professor at the Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia for five years from 1999 to 2004. Besides supervising a dozen of students for Ph.D. degrees in various disciplines of Mathematics namely Ring theory, Linear Algebra, Coding theory, Graph theory, and Cryptography he is actively engaged in post-graduate teaching and research. Prof. Ashraf has completed many major research projects from the University Grants Commission, New Delhi, India,  the Department of Science and Technology (DST), New Delhi, India, and the National Board of Higher Mathematics, Mumbai, India. Currently, he is also working on major research projects from the National Board of Higher Mathematics and the Department of Science and Technology. He has visited several foreign countries to deliver Plenary/ Invited lectures in International Conferences / Seminars and also has been visiting Scientist for many years in the University of Maribor, Slovenia under the bilateral exchange Programme supported by the Slovenian-Indian joint working group on Scientific and Technological co-operation under the auspices of DST, India and MHEST, Republic of Slovenia. Prof Ashraf is Editors / Managing Editors of many reputed international mathematical journals.​

Vincenzo De Filippis is professor of Mathematics at University of Messina, Italy. After receiving his Ph.D. from the University of Messina in 1999, he was elected to the position of assistant professor in 2002, associate professor in 2014 and full professor in 2022. He is author and coauthor of about 150 research papers in several international journals, coauthor of the book "Advanced linear algebra with applications", published by Springer, coeditor of two  research volumes published in the book series "Springer Proceedings in Mathematics and Statistics" and coeditor of one research volume published in the book series "Proceedings in Mathematics", published by De Gruyter. He has been on a research visit to several institutions in Europe, Asia and Africa. His research interests include ring theory, theory of associative algebras, linear and multilinear algebra. His theoretical work is primarily aimed at studying the structure of algebras satisfying functional identities.
Nadeem ur Rehman is a Professor in the Department of Mathematics at Aligarh Muslim University (AMU), Aligarh, India. After completing a PhD from Aligarh Muslim University in 2000, he was selected for a Postdoctoral Fellowship at the DAAD (Deutscher Akademischer Austausch Dienst) at the University of Kaiserslautern, Germany from August 01, 2001, to January 31, 2003. He joined the Aligarh Muslim University as an Assistant Professor in November 2006 and finally Professor in 2018. Before joining AMU as an Assistant Professor, he worked as an Assistant Professor at Birla Institute of Technology and Sciences, Pilani, from 2003 to 2006. He has also served as Associate Professor at the Department of Mathematics, Taibah University, Al-Madinah, for two years, from 2015 to 2017. He is an author and co-author of more than 150 peer-reviewed research articles in internationally recognized and reputed journals. His research interests include Ring theory, the theory of associative algebra, Linear Algebra, Coding theory, Graph theory andCryptography. Prof. Rehman has completed many major research projects from the University Grants Commission, New Delhi, India, and the Department of Science and Technology (DST), New Delhi, India. Presently, he is working on two major research projects from the National Board of Higher Mathematics, Mumbai, India and the Council of Scientific & Industrial Research (CSIRHRDG), New Delhi, India. He had visited several foreign countries to deliver invited lectures at International conferences and seminars. He had been a Visiting Scientist for many years at the University of Maribor, Slovenia, under the bilateral exchange program supported by the Slovenian-Indian joint working group on Scientific and Technological cooperation under the auspices of the DST, India, and the Ministry of Higher Education Science and Technology (MHEST), Republic of Slovenia. Together with all the above achievements, He is also a life member of several Mathematical Societies.

Textul de pe ultima copertă

The book intends to be a collection of research papers on algebra and related topics, most of which were presented at the international "Workshop on Associative Rings and Algebras with additional structures (WARA22)". The purpose of the workshop WARA22 was to present the current state of the art both in the Theory of Lie structures of associative rings and algebras and in the Theory of functional identities in rings. The conference has emerged as a powerful forum offering researchers the opportunity to meet, get to know each other and discuss advances in ring theory, inspiring further research directions. The main topics covered refer to rings with involution, Lie and Jordan structures, rings and algebras arising under various constructions, modules, bimodules and ideals in associative algebras, behavior of derivations, automorphisms and other kinds of additive maps in rings and algebras. All the contributing authors are leading international academicians and researchers in their respective fields. The papers cover a wide range of topics in ring theory, group theory, matrix algebra and graph theory. The book will serve both the specialist looking for the latest results and the novice looking for the appropriate references to access the study and understanding of the results presented here.​

Caracteristici

Offers a comprehensive description of the state of the art of the theory of functional identities in rings Provides a series of open problems aimed at stimulating the reader to approach the study of ring theory Covers a wide range of ring theory topics with applications in various fields