466 research outputs found
Projective equivalence of ideals in Noetherian integral domains
Let I be a nonzero proper ideal in a Noetherian integral domain R. In this
paper we establish the existence of a finite separable integral extension
domain A of R and a positive integer m such that all the Rees integers of IA
are equal to m. Moreover, if R has altitude one, then all the Rees integers of
J = Rad(IA) are equal to one and the ideals J^m and IA have the same integral
closure. Thus Rad(IA) = J is a projectively full radical ideal that is
projectively equivalent to IA. In particular, if R is Dedekind, then there
exists a Dedekind domain A having the following properties: (i) A is a finite
separable integral extension of R; and (ii) there exists a radical ideal J of A
and a positive integer m such that IA = J^m.Comment: 20 page
Existence of dicritical divisors revisited
We characterize the dicriticals of special pencils. We also initiate higher
dimensional dicritical theory
- …