Divisibility in the Stone-Čech compactification

• Autorzy: Šobot B.

Identyfikatory

DOI

10.4467/20842589RM.15.004.3913

• Języki publikacji: EN

Abstrakty

EN

After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-Čech compactification βN, we establish some results about one of such extensions. This provides us with one possible divisibility relation on βN, │~, and we introduce a few more, defined in a natural way. For some of them we find equivalent conditions for divisibility. Finally, we mention a few facts about prime and irreducible elements of (βN, ·). The motivation behind all this is to try to translate problems in elementary number theory into βN.

Słowa kluczowe

EN

divisibility; Stone-Čech compactification; ultrafilter

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2015
• Tom: Vol. 50
• Strony: 53--66
• Opis fizyczny: Bibliogr. 1 poz.

Twórcy

autor

Šobot B.

• Department of Mathematics and Informatics University of Novi Sad Trg Dositeja Obradovi´ca 4, 21000 Novi Sad, Serbia

Bibliografia

• [1] N. Hindman, D. Strauss, Algebra in the Stone-Čech compactification, theory and applications. 2nd revised and extended edition, De Gruyter, 2012.