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001-es BibID:	BIBFORM021436
Első szerző:	Bérczes Attila (matematikus)
Cím:	Multiply monogenic orders / Attila Bérczes, Jan-Hendrik Evertse, Kálmán Győry
Dátum:	2013
ISSN:	0391-173X 2036-2145
Megjegyzések:	Let O be an order in an algebraic number field K, i.e., a ring with quotient field K which is contained in the ring of integers of K. The order O is called monogenic, if it is of the shape Z[w], i.e., generated over the rational integers by one element. By a result of Győry (1976), the set of w with Z[w]=O is a union of finitely many equivalence classes, where two elements v,w of O are called equivalent if v+w or v-w is a rational integer. An order O is called k times monogenic if there are at least k different equivalence classes of w with Z[w]=O, and precisely k times monogenic if there are precisely k such equivalence classes. It is known that every quadratic order is precisely one time monogenic, while in number fields of degree larger than 2, there may be non-monogenic orders. In this paper we study orders which are more than one time monogenic. Our first main result is, that in any number field K of degree at least 3 there are only finitely many three times monogenic orders. Next, we define two special types of two times monogenic orders, and show that there are number fields K which have infinitely many orders of these types. Then under certain conditions imposed on the Galois group of the normal closure of K, we prove that K has only finitely many two times monogenic orders which are not of these types. We give some immediate applications to canonical number systems. Further, we prove extensions of our results for domains which are monogenic over a given domain A of characteristic 0 which is finitely generated over Z.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk monogenic orders power integral bases canonical number systems
Megjelenés:	Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. - 12 : 2 (2013), p. 467-497. -
További szerzők:	Evertse, Jan-Hendrik (1958-) Győry Kálmán (1940-) (matematikus)
Pályázati támogatás:	OTKA-T67580 OTKA OTKA-T75566 OTKA OTKA-100339 OTKA János Bolyai Research Scholarship Egyéb TÁMOP-4.2.1./B-09/1/KONV-2010-0007 TÁMOP
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