UID:
almahu_9947360003902882
Format:
Online-Ressource (500 p)
Edition:
Online-Ausg. 2011 Electronic reproduction; Available via World Wide Web
ISBN:
9783110154207
Series Statement:
De Gruyter Expositions in Mathematics v.27
Note:
Description based upon print version of record
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10.3 Homomorphisms from T* into S*10.4 Isomorphisms on Principal Ideals; Notes; 11 The Rudin-Keisler Order; 11.1 Connections with Right Cancelability; 11.2 Connections with Left Cancelability in N*; 11.3 Further Connections with the Algebra of ßS; 11.4 The Rudin-Frolík Order; Notes; 12 Ultrafilters Generated by Finite Sums; 12.1 Martin's Axiom; 12.2 Strongly Summable Ultrafilters - Existence; 12.3 Strongly Summable Ultrafilters - Independence; 12.4 Algebraic Properties; Notes; 13 Multiple Structures in ßS; 13.1 Sums Equal to Products in ßZ; 13.2 The Distributive Laws in ßZ.
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13.3 Ultrafilters on R Near 013.4 Left and Right Continuous Extensions; Notes; III. Combinatorial Applications; 14 The Central Sets Theorem; 14.1 Van der Waerden's Theorem; 14.2 The Hales-Jewett Theorem; 14.3 The Commutative Central Sets Theorem; 14.4 The Noncommutative Central Sets Theorem; 14.5 Combinatorial Characterization; Notes; 15 Partition Regularity of Matrices; 15.1 Image Partition Regular Matrices; 15.2 Kernel Partition Regular Matrices; 15.3 Kernel Partition Regularity Over N; 15.4 Image Partition Regularity Over N; 15.5 Matrices with Entries from Fields; Notes.
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16 IP, IP*, Central, and Central* Sets.
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3.5 Uniform Limits via Ultrafilters3.6 The Cardinality of ßD; Notes; Closing Remarks; 4 ßS; 4.1 Extending the Operation to ßS; 4.2 Commutativity in ßS; 4.3 S*; 4.4 K(ßS) and Its Closure; Notes; 5 ßS and Ramsey Theory; 5.1 Ramsey Theory; 5.2 Idempotents and Finite Products; 5.3 Sums and Products in N; 5.4 Adjacent Finite Unions; 5.5 Compactness; Notes; II. Algebra of ßS; 6 Ideals and Commutativity in ßS; 6.1 The Semigroup H; 6.2 Intersecting Left Ideals; 6.3 Numbers of Idempotents and Ideals; 6.4 Weakly Left Cancellative Semigroups; 6.5 Semiprincipal Left Ideals; 6.6 Principal Ideals in ßZ.
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6.7 Ideals and DensityNotes; 7 Groups in ßS; 7.1 Zelenuk's Theorem; 7.2 Semigroups Isomorphic to H; 7.3 Free Semigroups and Free Groups in ßS; Notes; 8 Cancellation; 8.1 Cancellation Involving Elements of S; 8.2 Right Cancelable Elements in ßS; 8.3 Right Cancellation in ßN and ßZ; 8.4 Left Cancelable Elements in ßS; 8.5 Compact Semigroups; Notes; 9 Idempotents; 9.1 Right Maximal Idempotents; 9.2 Topologies Defined by Idempotents; 9.3 Chains of Idempotents; 9.4 Identities in ßS; Notes; 10 Homomorphisms; 10.1 Homomorphisms to the Circle Group; 10.2 Homomorphisms from ßT into S*.
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I. Background Development; Notation; 1 Semigroups and Their Ideals; 1.1 Semigroups; 1.2 Idempotents and Subgroups; 1.3 Powers of a Single Element; 1.4 Ideals; 1.5 Idempotents and Order; 1.6 Minimal Left Ideals; 1.7 Minimal Left Ideals with Idempotents; Notes; 2 Right Topological Semigroups; 2.1 Topological Hierarchy; 2.2 Compact Right Topological Semigroups; 2.3 Closures and Products of Ideals; 2.4 Semitopological Semigroups; 2.5 Ellis' Theorem; Notes; 3 ßD; 3.1 Ultrafilters; 3.2 The Topological Space ßD; 3.3 Stone-Cech Compactification; 3.4 More Topology of ßD.
Additional Edition:
ISBN 9783110809220
Language:
English
Keywords:
Electronic books
DOI:
10.1515/9783110809220
URL:
http://dx.doi.org/10.1515/9783110809220
