03084nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001600167072002300183072001500206100007700221245015100298250001800449264006900467300004400536336002600580337002600606338003600632347002400668490006300692505008900755520108100844650001801925650001301943650001701956650002401973650002101997650003802018650005102056650001302107650001702120650004002137650002102177700007902198710003402277773002602311776003602337776003602373776003602409830006302445856004602508978-3-031-42891-3DE-He21320251030111507.0cr nn 008mamaa240311s2024    sz |    s    |||| 0|eng d  a97830314289137 a10.1007/978-3-031-42891-32doi 4aQA174-183 7aPBG2bicssc 7aMAT0020102bisacsh 7aPBG2thema1 aPetrich, Mario.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aCompletely Regular Semigroup Varietiesh[electronic resource] :bA Comprehensive Study with Modern Insights /cby Mario Petrich, Norman R. Reilly.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXIV, 238 p. 47 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSynthesis Lectures on Mathematics & Statistics,x1938-17510 aFully Invariant Relations -- Kernel and Trace Relations -- Bands -- Polák Theorem.  aThis 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. 0aGroup theory. 0aAlgebra. 0aMathematics. 0aMathematical logic. 0aAlgebraic logic.14aGroup Theory and Generalizations.24aOrder, Lattices, Ordered Algebraic Structures.24aAlgebra.24aMathematics.24aMathematical Logic and Foundations.24aAlgebraic Logic.1 aReilly, Norman R.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303142890608iPrinted edition:z978303142892008iPrinted edition:z9783031428937 0aSynthesis Lectures on Mathematics & Statistics,x1938-175140uhttps://doi.org/10.1007/978-3-031-42891-3