This proceedings is a collection of research papers on algebra and related topics, most of which were presented at the International Conference on Algebra and Related Topics with Applications (ICARTA-19), held at the Department of Mathematics, Aligarh Muslim University, Aligarh, India, from 1719 December 2019. It covers a wide range of topics on ring theory, coding theory, cryptography, and graph theory. In addition to highlighting the latest research being done in algebra, the book also addresses the abundant topics of algebra particularly semigroups, groups, derivations in rings, rings and modules, group rings, matrix algebra, triangular algebra, polynomial rings and lattice theory. Apart from these topics, the book also discusses applications in cryptology, coding theory, and graph theory.

Contains select chapters on algebra and related topics Discusses a wide range of topics on ring theory, coding theory, cryptography, and graph theory Focuses on applications in cryptology, coding theory, and graph theory

Autorentext

MOHAMMAD ASHRAF is Chairman and Professor at the Department of Mathematics, Aligarh Muslim University (AMU), Aligarh, India. He is also Dean, the Faculty of Science, AMU, Aligarh, India. He received his Ph.D. degree in mathematics from AMU, and started teaching at the Department of Mathematics, AMU, in the year 1986. He had made substantial contributions to ring theory and algebras, linear algebra, coding theory, graph theory, and cryptography. He proved several exemplary results and published them in internationally reputed journals. He has published more than 200 peer-reviewed scientific articles. He has organized several International conferences and edited five edited volumes and conference proceedings. Professor Ashraf has successfully completed many major research projects from the UGC, DST, and NBHM, India. He had visited several foreign countries to deliver plenary and invited lectures at international conferences and seminars. He had been Visiting Scientist for many years in the University of Maribore, Slovenia, under the bilateral exchange program supported by Slovenian-Indian joint working group on scientific and technological co-operation under the auspices of the DST, India, and the Ministry of Higher Education Science & Technology (MHEST), Republic of Slovenia. Together with all the above achievements, Prof. Ashraf is Editor and Managing Editor of many reputed international mathematical journals and life member of several mathematical societies. ASMA ALI is Professor at the Department of Mathematics, Aligarh Muslim University (AMU), Aligarh, India. She joined the Department of Mathematics at AMU, in 1995, as a faculty member and has been serving the department since then. She was awarded Senior Research Fellowship from UGC, New Delhi, and successfully completed her PhD in 1991. Professor Asma has made valuable contributions in her field of research and has published a number of papers in reputed international journals, which are being cited in India and abroad. Very recently, she has been selected for LEAP (Leadrership Academicians Programme) under MHRD scheme Pandit Madan Mohan Malaviya National Mission on Teachers and Teaching (PMMMNMTT), domestic training at CALEM, India, 16-30 December 2019, and foreign training from 15-22 February 2020 at Monash University, Melbourne, Australia. Professor Asma Ali has received honor of recognition for her contribution and achievements as successful professional by the International Society of Women in Science and has been a council member of Indian Mathematical Society. She is also a life member of many organizations including American Mathematical Society and Indian Science Congress.

VINCENZO DE FILIPPIS is Associate Professor at the Department of Mathematics, University of Messina, Italy. He received his PhD degree in mathematics (in 1999) from the University of Messina. He is an author and coauthor of more than 100 research papers published in several journals of repute 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 algebra. 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. A coeditor of various edited volumes, he is member of the Italian Mathematical Society (UMI) and the National Society of Algebraic and Geometric Structures and their Applications (GNSAGA-INDAM).

Inhalt

A. Abbasi, M. R. Mozumder and A. Jabeen, Characterization of b-generalized derivations in rings with involution.- M. S. Akhtar and M. A. Ansari, Jordan generalized n-derivations of unital algebras containing idempotents.- R. Alam, Variational analysis of approximate defective eigenvalues.- A. Ali, Structure of prime near rings with multiplicative generalized derivations.- R. A. Khaled Assaad, w-fp-projective modules and dimension.- L. Carini, Vincenzo De Filippis, Central values of X-generalized skew derivations on right ideals in prime rings.- H. Chimal-Dzul, Commutative polynomial rings which are principal ideal rings.- Vincenzo De Filippis, F. Rania, Two remarks on generalized skew derivations in prime rings.- U. Dempwolff, Dimensional dual hyperovals-An updated survey.- A. Gaur and R. Kumar, A note on FMS modules and FCP extensions.- S. Huang, Generalized derivations of - prime rings.- P. Kanwar, M. Khatkar and R. K. Sharma, Basic one sided ideals of Leavitt path algebras over commutative rings.- A. N. Khan, S. Ali, A. Abbasi, M. Ayedh, On certain -differntial identities in prime rings with involution.- M. S. Khan, On b-generalized derivations in prime rings.- D. Kumar, B. Bhushan, Commutativity of -prime rings with generalized derivation on Jordan ideals.- S Michael, P.G. Romeo, Local subsemigroups and variants of some classes of semigroups.- H. EL Mir, B. Nejjar, L. Oukhtite, On traces of permuting nderivations on prime ideals.- S. K. Nimbhorkar, Deepali B. Banswal, Closed weak supplemented lattices.- J. K. Park, S. T. Rizvi, , On Compatible Ring Structures of the Injective Hull of a Ring.- M. Arif Raza, M. S. Khan, N. ur Rehman, On Commutators Involving Derivations and Automorphisms in Prime Rings.- J. Roseline, M. K. Patel, Modules invariant under clean endomorphisms of their injective hulls.- A. Sabharwal, R. Sharma, P. Yadav, A note on central idempotents in finite group rings of symmetric groups.- G. Scudo, ordan product preserving generalized skew derivations on Lie ideals.- M. A. Siddeeque, Ali Ahmed Abdullah, N. Khan, Prime rings with generalized derivations and power values on Lie ideals.- J. Vukman, I. Kosi-Ulbl, On certain identity related to Jordan -derivations in standard operator algebras.- S. Ghorpade, R. Ludhani, On The Purity of Resolutions of Stanley-Reisner Rings Associated to Reed-Muller Codes.- G. Mohammad, N. Khan, A. Khan, Skew Constacyclic codes over Fq + vFq.- Om Prakash, H. Islam, A. Ghosh, yclic and LCD codes over a finite commutative semi-local ring.- M. Ashraf, M. Kumar, Some recent results on the graphs of finite dimensional vector spaces: A survey.- P. Aydogdu, J. Diaz Boils, Sergio R. LopezPermouth, Two Value Graph Magma Algebras and Amenability.- A. Badawi, Yasmine El-Ashi, Graph of linear transformations over R.- S. Pirzada, Bilal A. Rather, Rezwan Ul Shaban, M. Imran Bhat, On distance Laplacian (signless) eigenvalues of commuting graphs of dihedral and dicyclic groups.- V. Rabikka, T. Asir, M. Evangeline Pratibha, Eigenvalues and wiener index of graphs over rings: A survey.- N. Ur Rehman, Mohd. Nazim, Junaid Nisar, On a new extension of annihilating-ideal graph of commutative rings.- K. Selvakumar, J. Beautlin Jemi, Nadeem ur Rehman, Spectrum of the 3-zero-divisor hypergraph of some classes of local rings.- T. Tamizh Chelvam, Com…