Completely Regular Semigroup Varieties
Applications and Advanced Techniques
Sorozatcím: Synthesis Lectures on Mathematics & Statistics;
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18 151 Ft
Beszerezhetőség
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A termék adatai:
- Kiadás sorszáma 2024
- Kiadó Springer
- Megjelenés dátuma 2025. február 5.
- Kötetek száma 1 pieces, Book
- ISBN 9783031488245
- Kötéstípus Keménykötés
- Terjedelem198 oldal
- Méret 240x168 mm
- Nyelv angol
- Illusztrációk 31 Illustrations, black & white 685
Kategóriák
Rövid leírás:
This book presents further developments and applications in the area of completely regular semigroup theory, beginning with applications of Polák?s theorem to obtain detailed descriptions of various kernel classes including the K-class covers of the kernel class of all bands. The important property of modularity of the lattice of varieties of completely regular semigroups is then employed to analyse various principal sublattices. This is followed by a study of certain important complete congruences on the lattice; the group, local and core relations. The next chapter is devoted to a further treatment of certain free objects and related word problems. There are many constructions in the theory of semigroups. Those that have played an important role in the theory of varieties of completely regular semigroups are presented as they apply in this context. The mapping that takes each variety to its intersection with the variety of bands isa complete retraction of the lattice of varieties of completely regular semigroups onto the lattice of band varieties and so induces a complete congruence for which every class has a greatest member. The sublattice generated by these greatest members is then investigated with the help of many applications of Polák?s theorem. The book closes with a fascinating conjecture regarding the structure of this sublattice.
Hosszú leírás:
This book presents further developments and applications in the area of completely regular semigroup theory, beginning with applications of Polák?s theorem to obtain detailed descriptions of various kernel classes including the K-class covers of the kernel class of all bands. The important property of modularity of the lattice of varieties of completely regular semigroups is then employed to analyse various principal sublattices. This is followed by a study of certain important complete congruences on the lattice; the group, local and core relations. The next chapter is devoted to a further treatment of certain free objects and related word problems. There are many constructions in the theory of semigroups. Those that have played an important role in the theory of varieties of completely regular semigroups are presented as they apply in this context. The mapping that takes each variety to its intersection with the variety of bands is a complete retraction of the lattice of varieties of completely regular semigroups onto the lattice of band varieties and so induces a complete congruence for which every class has a greatest member. The sublattice generated by these greatest members is then investigated with the help of many applications of Polák?s theorem. The book closes with a fascinating conjecture regarding the structure of this sublattice.
Tartalomjegyzék:
General Sublattices of L(CR).- Neutrality and Intervals.- Free Objects.- Constructions.- Canonical Varieties.
Több
