RT Journal Article
T1 Arf closure relative to a divisorial valuation and transversal curves
A1 Campillo, Antonio
A1 Castellanos Peñuela, Julio Antonio
AB A subring of a discrete valuation ring Rv is called an Rv-Arf ring if it satisfies a certain condition first considered by C. Arf some forty-five years ago. Let A be any subring of Rv and let I be an ideal of A. The operation of the blow up of A at I along the valuation v, and the Arf closure of A with respect to v are explained. Their algebraic structure and main properties are studied. It is shown that, under some assumptions, the family of Arf subrings of Rv satisfies the ascending chain condition. The relation between Arf subrings of Rv and strictly closed subrings of Rv is studied. In the last section the geometrical interpretation of the Arf closure is given.
PB Johns Hopkins Univ Press
SN 0002-9327
YR 1994
FD 1994
LK https://hdl.handle.net/20.500.14352/58374
UL https://hdl.handle.net/20.500.14352/58374
LA eng
NO Accion Integrada Hispano Alemana
NO DGICYT
DS Docta Complutense
RD 10 may 2025