Semigroups, Algebras and Operator Theory

This book discusses recent developments in semigroup theory and its applications in areas such as operator algebras, operator approximations and category theory. All contributing authors are eminent researchers in their respective fields, from across the world. Their papers, presented at the 2014 International Conference on Semigroups, Algebras and Operator Theory in Cochin, India, focus on recent developments in semigroup theory and operator algebras. They highlight current research activities on the structure theory of semigroups as well as the role of semigroup theoretic approaches to other areas such as rings and algebras. The deliberations and discussions at the conference point to future research directions in these areas. This book presents 16 unpublished, high-quality and peer-reviewed research papers on areas such as structure theory of semigroups, decidability vs. undecidability of word problems, regular von Neumann algebras, operator theory and operator approximations. Interested researchers will find several avenues for exploring the connections between semigroup theory and the theory of operator algebras.

Autorentext

P.G. ROMEO is professor and head of the Department of Mathematics at the Cochin University of Science and Technology (CUSAT), Kochi, Kerala, India. His major research interests are in semigroups theory, representation theory, universal algebras and category theory. He earned his PhD from the University of Kerala in 1993 under the guidance of Professor K.S.S. Nambooripad. During his illustrious carrier as a researcher and a professor for over two decades, Prof. Romeo taught a wide variety of courses both for undergraduate and graduate level. He is also guiding students for doctoral research. He has published research articles with various peer reviewed international mathematics journals as well as given invited talks at various international and national conferences.

JOHN MEAKIN is the Milton Mohr Professor of Mathematics at the University of Nebraska-Lincoln, USA. He served as the chair of the Department of Mathematics at Nebraska during 2003-2011. His primary research interests are modern algebra and theoretical computer science, with particular focus on the algebraic theory of semigroups and geometric group theory. He teaches a wide variety of courses ranging from freshman level calculus to advanced graduate courses in algebra and topology. Professor Meakin has published extensively in peer reviewed international mathematics journals and served for 20 years as managing editor of International Journal of Algebra and Computation. Elected in 2014 as a Fellow of the American Mathematical Society, Professor Meaking has given around 200 invited lectures at conferences and universities around the world and has held extended visiting positions in Australia, Belgium, France, India, Israel, Italy, Spain, and the USA.

A.R. RAJAN is the emeritus professor at the Department of Mathematics, University of Kerala, India. He earned his PhD and MA (Russian language) fromKerala University. He also held positions such as member of the senate and syndicate of the University of Kerala and chairman of the board of studies in mathematics. Professor Rajan has also served as member board of studies at Cochin University of Science and Technology, University of Calicut, Mahatma Gandhi University, Manonmaiam Sundernar University and Periyar University. He has participated conferences held in Austria, Hungary, United Kingdom, Thailand and Vietnam and published in peer reviewed journals such as Semigroup Forum, Quarterly Journal of Mathematics, Journal of Pure and Applied Mathematics. His areas of research interests include structure theory of semigroups, matrix semigroups, topological semigroups, theory of semirings and automata theory.

Inhalt
Chapter 1. Decidability vs. Undecidability of the Word Problem in Amalgams of Inverse Semigroups.- Chapter 2. A Nonfinitely Based Semigroup of Triangular Matrices.- Chapter 3. Regular Elements in Von Neumann Algebras.- Chapter 4. LeftRight Clifford Semigroups.- Chapter 5. Certain Categories Derived from Normal Categories.- Chapter 6. Semigroup Ideals and Permuting 3-derivations in Prime Near Rings.- Chapter 7. Biordered Sets and Regular Rings.- Chapter 8. Topological Rees Matrix Semigroups.- Chapter 9. Prime Fuzzy Ideals, Completely Prime Fuzzy Ideals of Po-Gamma-Semigroups based on Fuzzy Points.- Chapter 10. Radicals and Ideals of Affine Near Semirings over Brandt Semigroups.- Chapter 11. Operator Approximation.- Chapter 12. The Null Space Theorem.- Chapter 13. Role of Hilbert Scales in Regularization Theory.- Chapter 14. On Three-Space Problems for Certain Classes of C - Algebras.- *Chapter 15. Spectral Approximation of Bounded Self- Adjoint Operators- A Short Survey.- Chapter 16. On k-Minimal and k-Maximal Operator Space Structures.