Algebra Without Borders : Classical and Constructive Semigroups and Applications

著者名：Mitrović, Melanija (EDT)/Hounkonnou, Mahouton Norbert (EDT)

Springer（2025/09/26発売）

• 言語：ENG
• ISBN：9783031864766
• eISBN：9783031864773

Description

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.

Table of Contents

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 Krasner’s Graded to Krasner – Vuković’s 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 햘햑(2)-type.