This book addresses the well-known capability and flexibility of classical and constructive semigroups (inherited from algebraic structures), to model, solve problems in extremely diverse situations, and develop interesting new algebraic ideas with many applications and connections to other areas of mathematics (logic, biomathematics, analysis, geometry, etc.), natural sciences, engineering and life sciences, interconnections between semigroups, cognitive sciences, social sciences, arts and humanities. The book promotes the idea that algebra came at the core of interdisciplinarity, belongs to all life disciplines, and serves in a variety of mathematics applications. It focuses on recent developments in classical and constructive semigroups, and other basic algebraic structures as well as on some of their potential applications in other fields. Further, it helps shed light on ways in which classical and constructive semigroups have been developing and applying in various domains, and extended with other sciences. The content is based on contributions of an international team of renowned scientists with expertise in different disciplines of mathematics, classical and constructive semigroups, other algebraic structures and their applications in logic, cognitive sciences, linguistics, biology, machine learning, and collective phenomena.
Chapter 1: Three themes in the development of classical semigroup
theory.
Chapter 2: Introduction to inverse semigroups.
Chapter 3: A journey
through constructive inverse semigroups with apartness.
Chapter 4: On graph
inverse semigroups.
Chapter 5: Unification via projectivity in varieties of
hoops.
Chapter 6: From Krasners Graded to Krasner Vukovis Paragraded
Groups and Rings.
Chapter 7: Transformation semigroups and their
applications.
Chapter 8: Markov semigroup approach to evolution equations.-
Chapter 9: Inverse Semigroups and Omaha Kinship.
Chapter 10: Set-theoretical
considerations and zero-division
on hom-associative algebras.
Chapter 11: Hom-Lie Structure of Generalized
(2)-type.
Melanija Mitrovi is a Full Professor at the University of Ni, Serbia, having received her PhD degree at the same university. She works in the field of classical and constructive algebra. Her innovating work within the theory of constructive binary structures with apartness positions her among the pioneers of constructive mathematics in Serbia. She develops interdisciplinary research investigating applications of algebraic structures to problems in engineering space, social sciences and humanities. She is, also, the Head of the Center of Applied Mathematics of the Faculty of Mechanical Engineering Ni, CAM- FMEN (since 2019), a member of the Editorial Board of Mathematics in Mind, Springer; a member of the Fields Cognitive Science Network. She holds the status of Permanent Full Professor at the International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, Benin Republic. She has held visiting professor positions at Linköping University and Malardaren University, Sweden; Bar-Ilan University, Israel; TU Wien, Austria; UTAD and University of Minho, Portugal; and Politecnico di Milano, Italy.
Mahouton Norbert Hounkonnou is a Full Professor of Mathematics and Physics at the University of Abomey-Calavi, Benin Republic. His works deal with noncommutative and nonassociative mathematics and complexity, focusing on algebraic structures and geometric methods in integrable systems. He serves as member or associate editor of editorial boards for renowned journals and books series in mathematics and mathematical physics, such as Afrika Matematika (Springer), Mathematics in Mind (Springer), Fields Cognitive Science Network, the Peer Community In (PCI) Neuroscience, etc. He is member of several learned societies, including the Academy of Science of South Africa, the Hassan II Academy of Science and Technology (Morocco), the African Academy of Sciences, the World Academy of Sciences, the American Mathematical Society, London Mathematical Society, etc. He has received several prestigious international awards including, most recently, the 2023 AIP Tate Medal and the 2023 Yang Hui Prize for his seminal contributions to deformed quantum algebras.
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