noetherian ring meaning in Hindi

Examples

1. Consequently, an irreducible ideal of a Noetherian ring is primary.
2. A Noetherian ring does not necessarily have a dualizing module.
3. The integers, however, form a Noetherian ring which is not Artinian.
4. The decomposition does not hold in general for non-commutative Noetherian rings.
5. This is sufficient to guarantee that a right-Noetherian ring is right Goldie.
6. The Krull intersection theorem says that this cannot happen for a Noetherian ring .)
7. It has only been proven for special types of Noetherian rings, so far.
8. It has led to a better understanding of noncommutative rings, especially noncommutative Noetherian rings.
9. In a right noetherian rings; the result is known as Levitzky's theorem.
10. It is very hard to construct examples of Noetherian rings that are not universally catenary.