ISRAEL JOURNAL OF MATHEMATICS 174 (2009), 161–177 DOI: 10.1007/s11856-009-0107-9 A CHARACTERIZATION OF PROJECTIVE WEAK GALOIS EXTENSIONS BY J. N. Alonso ´ Alvarez Departamento de Matem´aticas, Universidad de Vigo, Campus Universitario Lagoas-Marcosende, E-36280 Vigo, Spain. e-mail: jnalonso@uvigo.es AND J. M. Fern´ andez Vilaboa Departamento de ´ Alxebra, Universidad de Santiago de Compostela, E-15771 Santiago de Compostela, Spain. e-mail: alvila@usc.es AND R. Gonz´ alez Rodr´ ıguez Departamento de Matem´atica Aplicada II, Universidad de Vigo, Campus Universitario Lagoas-Marcosende, E-36280 Vigo, Spain. e-mail: rgon@dma.uvigo.es AND M. P. L´ opez Departamento de ´ Alxebra, Universidad de Santiago de Compostela, E-15771 Santiago de Compostela, Spain. e-mail: puralo@usc.es Received July 19, 2006 and in revised form October 18, 2007 161