Prime ideals in three dimensional regular local rings
Tutor / directorPlanas Vilanova, Francesc d'Assís
Document typeMaster thesis
Rights accessOpen Access
The aim of this work is twofold. First we study a family of prime ideals, in the power series ring in three variables over a field, which need arbitrarily high number of generators. This family was introduced by T. T. Moh in the seventies. Second, and having in mind to generalize this phenomenon to any three dimensional regular local ring, we study the proof of the existence of a prime ideal minimally generated by four elements, in any regular local ring. This fact was recently stated by F. Planas. We conclude the present dissertation by extending this result to a prime ideal minimally generated by five elements.
DegreeMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)