Semigroups, Categories, and Partial Algebras

This book is a collection of selected papers presented at the International Conference on Semigroups and Applications, held at the Cochin University of Science and Technology, India, from December 9-12, 2019. This book discusses the recent developments in semigroups theory, category theory and the applications of these in various areas of research, including structure theory of semigroups, lattices, rings and partial algebras. This book presents chapters on ordering orders and quotient rings, block groups and Hall's relations, quotients of the Booleanization of inverse semigroup, Markov chains through semigroup graph expansions, polycyclic inverse monoids and Thompson group, balanced category and bundle category. This book will be of much value to researchers working in areas of semigroup and operator theory.

Autorentext
P. G. ROMEO is Professor and Head of the Department of Mathematics at Cochin University of Science and Technology (CUSAT), Kochi, Kerala, India. He earned his Ph.D. in Mathematics from the University of Kerala, India, in 1993, under the guidance of Prof. K. S. S. Nambooripad. His major research interests include semigroup theory, representation theory of groups and algebras, universal algebras and category theory. During his illustrious career as researcher and professor for three decades, Prof. Romeo taught a wide variety of courses ranging from freshman-level calculus to advanced graduate courses in algebra, representation theory and topology. He guides students for doctoral research and has been publishing extensively in peer-reviewed international mathematical journals. He has also given invited lecturers at various international and national conferences and is a member of the Indian Mathematical Society and the Executive Trustee to the Mathematics and Statistics Science Trust, Kerala.
MIKHAIL V. VOLKOV is Professor and Chair of the Department of Algebra and Theoretical Computer Science at the Institute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg, Russia,. With over 150 papers and influential survey articles, he has published textbooks in algebra, automata, combinatorics on words and formal languages. He is the managing editor of the Semigroup Forum, the main international journal in semigroup theory published by Springer and is also on the editorial boards of renowned international journals of mathematics. He has given around 100 invited lectures at conferences and has had extended visiting positions in Australia, Austria, China, Czech Republic, Finland, France, Germany, India, Israel, Italy, Poland and the USA. In 2017, Prof. Volkov was elected as a foreign member to the Finnish Academy of Science and Letter; and appointed as Mercator Professor at the University of Trier, Germany, by German Research Foundation in 2019.
A. R. RAJAN is Director of The State Institute of Encyclopedic Publications, Government of Kerala, India, and Former Professor and Head, Department of Mathematics, University of Kerala, India. He was Emeritus Professor under the Kerala State Council for Science Technology and Environment, during 2014 to 2016. He earned his Ph.D. in Mathematics from the University of Kerala, India, under the guidance of Prof. K. S. S. Nambooripad. He also holds master's degree in the Russian language. He held positions such as Member of the Senate and Syndicate of the University of Kerala and Chairman of the Board of Studies in Mathematics. He has participated in international conferences held in Portugal, the United Kingdom, Vietnam, Thailand, Hungary and Austria and has published in peer reviewed journals of repute. He is an editor of the Asian-European Journal of Mathematics. His areas of research include structure theory of semigroups, matrix semigroups, topological semigroups and automata theory. He is a member of the American Mathematical Society, Indian Mathematical Society, and Ramanujan Mathematical Society, and the honorary director of the Institute of Mathematical Research and Training (IMRT), Trivandrum, India.

Inhalt
A. Guterman, L. Márki, P. Shteyner, Ordering orders and quotient rings.- P. U. Anusha, Riyas and K. Geetha, A Study On Cayley Graphs of Full Transformation Semigroups.- A. M. Gaysian M. V. Volkov, Block groups and Hallrelations.- B. Yu , Z. Wang, K. Shum, Balanced Categories and the Biorder in Semigroups.- G. Kudryavtseva, Quotients of the booleanization of an inverse semigroup.- J. Kumar, S. Dalal, P. Pandey, On the structure of the commuting graph of Brandt semigroups.- J. Meakin, P. A. Azeef Mohammed A. R. Rajan, The mathematical work of KS S Nampooripad.- J. Rhodes, A. Schilling, Markov chains through semigroup graph expansions (a survey).- L. Carini, On various multiplicity free products of Schur functions.- Mário J. J. Branco, J. Carlos Costa, On identities over finite aperiodic semigroups with commuting idempotents.- M. V. Lawson, The polycyclic inverse monoids and the Thompson group revisited.- C. S. Preenu, A. R. Rajan, K. S. Zeenath, Category of principal left ideals of Normal bands.- P. G. Romeo, R. Jose, Category of chain bundles.- V. Yu Shaprynskii, B. M Vernikov, Cancellable elements in the lattice of overcommutative semigroup varieties.