Algebra and its Applications

This book discusses recent developments and the latest research in algebra and related topics. The book allows aspiring researchers to update their understanding of prime rings, generalized derivations, generalized semiderivations, regular semigroups, completely simple semigroups, module hulls, injective hulls, Baer modules, extending modules, local cohomology modules, orthogonal lattices, Banach algebras, multilinear polynomials, fuzzy ideals, Laurent power series, and Hilbert functions. All the contributing authors are leading international academicians and researchers in their respective fields. Most of the papers were presented at the international conference on Algebra and its Applications (ICAA-2014), held at Aligarh Muslim University, India, from December 15-17, 2014. The conference has emerged as a powerful forum offering researchers a venue to meet and discuss advances in algebra and its applications, inspiring further research directions.

Autorentext

S. TARIQ RIZVI is Professor and the Coordinator of Department of Mathematics, the Ohio State University (OSU), Lima, USA. After receiving his Ph.D. from McMaster University (Canada) in 1981 and teaching at the University of Waterloo (Canada), he joined OSU in 1982. A recipient of the Outstanding Scholar Award from OSU and a Fulbright Fellow Award from the Fulbright Board, Washington, DC, Professor Rizvi is world renowned for his research contributions to the theory of rings and modules. He has numerous research papers to his credit published in several international journals of high repute, published a monograph by Birkhäuser and coedited five research volumes with other reputed publishers. He also serves on editorial boards of ten international journals, including two as a managing or executive editor. Professor Rizvi has given over 120 invited talks at several national and international conferences, many as a plenary speaker. He has regularly organized sessions at a number of conferences including at the American Mathematical Society conferences and the Ohio State-Denison Math Conference series.

ASMA ALI is professor of mathematics at the Department of Mathematics, Aligarh Muslim University (AMU), Aligarh, India. She has made valuable contributions to mathematical research with publishing a number of papers in international journals of repute. She has been awarded the honor of recognition for the achievements as a successful professional at the International Women's Day at AMU in 2015. She is also life member of many organizations including the American Mathematical Society, the Indian Mathematical Society and the Indian Science Congress.

VINCENZO DE FILIPPIS is associate professor of mathematics at the University of Messina, Italy. He received the M.S. (1993) and Ph.D. (1999) degrees from the University of Messina. He is an author and coauthor of numerous professional publications and has been on research visits to several institutions in Europe, India, China and Turkey. 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.

Inhalt

Jae Koel Park and S. M. Tariq Rizvi: On some Classes of Module Hulls.- Akihiro Yamamura: Spined Product Decompositions of Orthocryptogroups.- Vincenzo de Filippis: Generalized Skew Derivations and g-Lie Derivations of Prime Rings.- Ashish Kumar Srivastava: Additive Representations of Elements in Rings: A Survey.- Shuliang Huang: Notes on Commutativity of Prime Rings.- Shervin Sahebi and V. Rahmani: Generalized Derivations on Rings and Banach Algebras.- Ravi A. Rao: A study of Suslin Matrices: Their Properties and Uses.- Shreedevi K. Masuti, Parangama Sarkar and J. K. Verma: Variation on the Grothendieck-Serre Formula for Hilbert Functions and Their Applications.- Tony Joseph Puthenpurakal: De Rham Cohomology of Local Cohomology Modules.- Manoj Kumar Yadav: Central Quotient Versus Commutator Subgroup of Groups.- Tamilselvi, A. Vidhya and B. Kethesan: Robinson-Schensted Correspondence for the Walled Brauer Algebras and the Walled Signed Brauer algebras.- M.K. Sen: - Semigroups: A Survey.- N. K. Thakare, B. N. Waphare and AvinashPatil: Comparability Axioms in Orthomodular Lattices and Rings with Involution.- A. R. Rajan: Structure theory of regular Semigroups using Categories.- P. G. Romeo and Akhila R.: Biorder Ideals and Regular Rings.- Asma Ali and Farhat Ali: Product of Generalized Semiderivation in Prime Near Rings.- Selvaraj and R. Saravanan: n-Strongly Gorenstein Projective and Injective Complexes.- Basudeb Dhara: Generalized Derivations with Nilpotent Values on Multilinear Polynomials in Prime Rings.- Manoj Kumar Patel: Properties of Semi-Projective Modules and Their Endomorphism Rings.- R. P. Sharma: L Labelling of Sets Under the Actions of Sn and An.- Anil Khainar and B. N. Waphare: Zero-Divisor Graphs of Laurent Polynomials and Laurent Power Series.- Basudeb Dhara, Asma Ali and Shahoor Khan:Pair of Generalized Derivations and Lie Ideals in Prime Rings.- T. Tamizh Chelvam, T. Asir and K. Selvakumar: On Domination in Graphs from Commutative Rings: A survey.- A. K. Chaturvedi: On Iso-Retractable Modules and Rings.- Azeef Muhammed P. A.: Normal Categories from Completely Simple Semigroups.- N. M. Khan and Mohd. Aasim Khan: Ordered Semigroups Characterize in Terms of Intuitionstic Fuzzy Ideals.- R. D. Giri: On a Problem of Satyanarayana Regarding the Recognizability of Codes.