Abstract
AbstractWe continue the research of an extension of the divisibility relation to the Stone‐Čech compactification . First we prove that ultrafilters we call prime actually possess the algebraic property of primality. Several questions concerning the connection between divisibilities in and nonstandard extensions of are answered, providing a few more equivalent conditions for divisibility in . Results on uncountable chains in are proved and used in a construction of a well‐ordered chain of maximal cardinality. Probably the most interesting result is the existence of a chain of type in . Finally, we consider ultrafilters without divisors in and among them find the greatest class.
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