A Comprehensive Study with Modern Insights Petrich, Mario. creator author. aut http://id.loc.gov/vocabulary/relators/aut Reilly, Norman R. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 1st ed. 2024. monographic eng

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electronic resource

access XIV, 238 p. 47 illus. online resource. This book is a unified treatment of the most important core developments in the theory of completely regular semigroup theory as it stands today. This volume focuses on the lattice of varieties of completely regular semigroups. Since any in-depth study of the lattice of varieties requires an understanding of free completely regular semigroups, the book begins by describing the free object on countably infinite sets and the properties of the lattice of fully invariant congruences on the free object. The authors introduce various associated relations and operators on the lattice of varieties of completely regular semigroups. Following that, the book covers the sublattice of varieties of bands with a focus on the influence of that sublattice on the structure of the whole lattice. The book concludes with the remarkable theorem due to Polák describing the whole lattice of varieties of completely regular as a subdirect product of lattices, some of which are well understood. The authors include recent advances, insights, results, and techniques throughout the book. Fully Invariant Relations -- Kernel and Trace Relations -- Bands -- Polák Theorem. by Mario Petrich, Norman R. Reilly. Group theory Algebra Mathematics Mathematical logic Algebraic logic Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Algebra Mathematics Mathematical Logic and Foundations Algebraic Logic QA174-183 9783031428913 https://doi.org/10.1007/978-3-031-42891-3 https://doi.org/10.1007/978-3-031-42891-3 240311 20251030111507.0 978-3-031-42891-3