irreducible ideal meaning in Hindi

Examples

1. Consequently, an irreducible ideal of a Noetherian ring is primary.
2. Moreover, while an ideal generated by a prime element is a prime ideal, it is not true in general that an ideal generated by an irreducible element is an irreducible ideal.
3. This is not true for irreducible ideals : an irreducible ideal may be generated by an element that is not an irreducible element, as is the case in \ mathbb Z for the ideal 4 \ mathbb Z : It is not the intersection of two strictly greater ideals.
4. This is not true for irreducible ideals : an irreducible ideal may be generated by an element that is not an irreducible element, as is the case in \ mathbb Z for the ideal 4 \ mathbb Z : It is not the intersection of two strictly greater ideals.