Representing the Smallest Ideal and it's closure in the semigroup ($β$N,.) as equivalence classes under the extension of divisibility relations

Salahddeen Khalifa

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arXiv · 1809.07395

Representing the Smallest Ideal and it's closure in the semigroup ($β$N,.) as equivalence classes under the extension of divisibility relations

Salahddeen Khalifa

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Abstract

In this paper we will prove that all the elements in the smallest ideal K($β$N) in the semigroup of the Stone Cech compactification ($β$N,.) of the discrete semigroup of natural numbers N under multiplication constitute a single equivalence class under the mid extension divisibility relation. And all the elements in the closure of the smallest ideal Cl($β$N) constitute a single equivalence class under the tilde extension divisibility relation.

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BibTeX RIS

Salahddeen Khalifa. 2018-09-19. Representing the Smallest Ideal and it's closure in the semigroup ($β$N,.) as equivalence classes under the extension of divisibility relations. https://arxiv.org/abs/1809.07395

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