Author
Liu, Yu-Han

Year
2010

The notion of gradient ideals in a power series algebra over a noetherian local ring is defined with basic properties studied.  A natural generalization, multi-gradient ideals'', and the algebra of potential functions associated to an arbitrary ideal are introduced.  Classification of multi-gradient ideals is given in the cases of principal ideals and monomial ideals by studying their algebras of potential functions.  Abstract examples of non-multi-gradient ideals and geometric examples of multi-gradient ideals are constructed.