| Popis: |
If R c T is an integral extension of domains and R is Noetherian, then T satisfies (the conclusion of the) generalized principal ideal theorem (or GPIT for short). An example is given of a twodimensional quasilocal domain R satisfying GPIT such that the integral closure of R is finite over R but does not satisfy GPIT. If a commutative ring R satisfies GPIT and an ideal / of R is generated by an i?-sequence, then R/I satisfies GPIT. If R is a Noetherian domain and G is a torsionfree abelian group, then R[G] satisfies GPIT. An example is given of a three-dimensional quasilocal KruU domain that does not satisfy GPIT because its maximal ideal is the radical of a 2-generated ideal. |
