2024-11-0920180092-787210.1080/00927872.2018.14488352-s2.0-85052201291http://dx.doi.org/10.1080/00927872.2018.1448835https://hdl.handle.net/20.500.14288/10571In this study, we find height bounds in the polynomial ring over the field of algebraic numbers to test the primality of an ideal. We also obtain height bounds in the arithmetic Nullstellensatz. We apply nonstandard analysis and hence our constants will be ineffective.MathematicsJournal Article1532-4125442620000023Q43204