The semigroup βℕ and its applications to number theory

Hindman, Neil

doi:10.1515/9783110856040.347

Cited by 8 publications

(2 citation statements)

References 22 publications

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“…As a compact right topological semigroup PS has idempotents [6,Corollary 2.10]. The existence of these idempotents, especially idempotents in the smallest ideal of PS, has important combinatorial consequences (See [11] and [15], for example).…”

Section: Introductionmentioning

confidence: 99%

Compact subsemigroups of (βℕ, +) containing the idempotents

Hindman

Strauss²

1996

Proceedings of the Edinburgh Mathematical Society

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The space /?N is the Stone-Cech compactification of the discrete space of positive integers. The set of elements of /}N which are in the kernel of every continuous homomorphism from /?N to a topological group is a compact semigroup containing the idempotents. At first glance it would seem a good candidate for the smallest such semigroup. We produce an infinite nested sequence of smaller such semigroups all defined naturally in terms of addition on N.1991 Mathematics subject classification: 22A15.

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Section: Introductionmentioning

confidence: 99%

Compact subsemigroups of (βℕ, +) containing the idempotents

Hindman

Strauss²

1996

Proceedings of the Edinburgh Mathematical Society

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“…In addition, the algebraic structure has been often useful in obtaining results in Ramsey Theory. See for example the survey [13]. We are concerned in this paper with cancellation in PS.…”

Section: Introductionmentioning

confidence: 99%

Cancellation in the Stone–Čech compactification of a discrete semigroup

Hindman

Strauss

1994

Proceedings of the Edinburgh Mathematical Society

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We investigate both left and right cancellation in the Stone-tech compactiflcation fSS of a discrete semigroup S, obtaining several results for arbitrary semigroups 5 and others for more restricted semigroups. In particular, if S is the semigroup of injective functions from a set to itself we determine precisely which pairs x, y and S have some pefiS with px = py. We also obtain several new results about right cancellation in (/?N, +).

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An Illustration of the Power of Structure Theory

Hofmann

2000

Papers in Honour of Bernhard Banaschewski

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The semigroup βℕ and its applications to number theory

Cited by 8 publications

References 22 publications

Compact subsemigroups of (βℕ, +) containing the idempotents

Compact subsemigroups of (βℕ, +) containing the idempotents

Cancellation in the Stone–Čech compactification of a discrete semigroup

An Illustration of the Power of Structure Theory

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