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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Increasing chains of ideals and orbit closures in $ \beta{\bf Z}$


Authors: Neil Hindman, Jan van Mill and Petr Simon
Journal: Proc. Amer. Math. Soc. 114 (1992), 1167-1172
MSC: Primary 54D35
MathSciNet review: 1089407
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Abstract: Given any discrete semigroup $ (S, + )$, there is an extension of the operation to $ \beta S$ making $ (\beta S, + )$ a left topological semigroup. The aim of this paper is, among other things, to prove that there exist strictly increasing chains of principle left ideals and of principal closed ideals in $ (\beta \mathbb{Z}, + )$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1089407-5
PII: S 0002-9939(1992)1089407-5
Keywords: Shift function, $ \beta \mathbb{Z}$, ideal, semigroup
Article copyright: © Copyright 1992 American Mathematical Society