noetherian ring उदाहरण वाक्य

उदाहरण वाक्य

1. Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules coincide.
2. For example, every quasi-projective scheme over a Noetherian ring has the resolution property.
3. For commutative Noetherian rings, this is the same as the definition using chains of prime ideals.
4. That follows because the rings of algebraic geometry, in the classical sense, are Noetherian rings.
5. Both facts imply that a finitely generated commutative algebra over a Noetherian ring is again a Noetherian ring.
6. Both facts imply that a finitely generated commutative algebra over a Noetherian ring is again a Noetherian ring.
7. This property suggests a deep theory of dimension for Noetherian rings beginning with the notion of the Krull dimension.
8. All quotient rings of a Noetherian ring are Noetherian, but that does not necessarily hold for its subrings.
9. Over a commutative Noetherian ring, this gives a particularly nice understanding of all injective modules, described in.
10. A "'Gorenstein ring "'is a commutative Noetherian ring such that each Cohen Macaulay.