On Z-Modules of Algebraic Integers
نویسندگان
چکیده
Let q be an algebraic integer of degree d ≥ 2. Consider the rank of the multiplicative subgroup of C generated by the conjugates of q. We say q is of full rank if either the rank is d− 1 and q has norm±1, or the rank is d. In this paper we study some properties of Z[q] where q is an algebraic integer of full rank. The special cases of when q is a Pisot number and when q is a Pisot-cyclotomic number are also studied. There are four main results. (1) If q is an algebraic integer of full rank and n is a fixed positive integer, then there are only finitely many m such that disc ` Z[qm] ́
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تاریخ انتشار 2009