03403nam a22005895i 4500 978-3-031-42891-3 DE-He213 20251030111507.0 cr nn 008mamaa 240311s2024 sz | s |||| 0|eng d 9783031428913 978-3-031-42891-3 10.1007/978-3-031-42891-3 doi QA174-183 PBG bicssc MAT002010 bisacsh PBG thema Petrich, Mario. author. aut http://id.loc.gov/vocabulary/relators/aut 72654 Completely Regular Semigroup Varieties [electronic resource] : A Comprehensive Study with Modern Insights / by Mario Petrich, Norman R. Reilly. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIV, 238 p. 47 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Synthesis Lectures on Mathematics & Statistics, 1938-1751 Fully Invariant Relations -- Kernel and Trace Relations -- Bands -- Polák Theorem. 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. Group theory. 70149 Algebra. 1501 Mathematics. 65523 Mathematical logic. 66195 Algebraic logic. 72655 Group Theory and Generalizations. 70154 Order, Lattices, Ordered Algebraic Structures. 69500 Algebra. 1501 Mathematics. 65523 Mathematical Logic and Foundations. 66198 Algebraic Logic. 72656 Reilly, Norman R. author. aut http://id.loc.gov/vocabulary/relators/aut 72657 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031428906 Printed edition: 9783031428920 Printed edition: 9783031428937 Synthesis Lectures on Mathematics & Statistics, 1938-1751 https://doi.org/10.1007/978-3-031-42891-3 ZDB-2-SXSC 58187 58187