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Preprint Number 929
929. Junguk Lee
Some arithmetic properties on nonstandard rationals
Submission date: 22 September 2015.
In this note, we study some arithmetics of nonstandard rationals. We show that the ranks of nonsingular elliptic curves over rational field are uniformly finitely bounded if and only if weak Mordell-Weil property holds in all(some) ℵ_1-saturated nonstandard rational number fields. We give an infinite factorization theorem on a nonstandard rational field using valuations induced from primes of a nonstandard integer ring, and we classify maximal and prime ideals in the nonstandard integer ring in terms of maximal filter on the set of primes and ordered semigroups of the valuation semigroup induced from maximal ideals.
Mathematics Subject Classification: 03H15, 11G05, 11U10
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