Central Sets Theorem on noncommutative semigroups

Let D be a directed set without maximal element, S be an infinite semigroup and DS be the collection of all functions from D into S. It is shown that for a commutative semigroup S, A⊆S is a C-set with respect to NS if and only if A is a C-set with respect to DS. We investigate the Central Sets Theor...

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Bibliographic Details
Published inIndagationes mathematicae Vol. 30; no. 2; pp. 329 - 339
Main Authors Keshavarzian, J., Tootkaboni, M.A.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.03.2019
Elsevier Science Ltd
Subjects
[formula omitted]-set
Central Sets Theorem
Piecewise syndetic set
Stone–[formula omitted]ech compactification
Theorems
Central Sets Theorem
Stone–Cˇech compactification
Piecewise syndetic set
C-set
J-set
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Summary:Let D be a directed set without maximal element, S be an infinite semigroup and DS be the collection of all functions from D into S. It is shown that for a commutative semigroup S, A⊆S is a C-set with respect to NS if and only if A is a C-set with respect to DS. We investigate the Central Sets Theorem for arbitrary semigroups. In fact the Central Sets Theorem is stated with respect to SS for arbitrary semigroups.
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2018.12.003