noetherian ring वाक्य
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- Consequently, an irreducible ideal of a Noetherian ring is primary.
- A Noetherian ring does not necessarily have a dualizing module.
- The integers, however, form a Noetherian ring which is not Artinian.
- The decomposition does not hold in general for non-commutative Noetherian rings.
- This is sufficient to guarantee that a right-Noetherian ring is right Goldie.
- The Krull intersection theorem says that this cannot happen for a Noetherian ring .)
- It has only been proven for special types of Noetherian rings, so far.
- It has led to a better understanding of noncommutative rings, especially noncommutative Noetherian rings.
- In a right noetherian rings; the result is known as Levitzky's theorem.
- It is very hard to construct examples of Noetherian rings that are not universally catenary.
- Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules coincide.
- For example, every quasi-projective scheme over a Noetherian ring has the resolution property.
- For commutative Noetherian rings, this is the same as the definition using chains of prime ideals.
- That follows because the rings of algebraic geometry, in the classical sense, are Noetherian rings.
- Both facts imply that a finitely generated commutative algebra over a Noetherian ring is again a Noetherian ring.
- Both facts imply that a finitely generated commutative algebra over a Noetherian ring is again a Noetherian ring.
- This property suggests a deep theory of dimension for Noetherian rings beginning with the notion of the Krull dimension.
- All quotient rings of a Noetherian ring are Noetherian, but that does not necessarily hold for its subrings.
- Over a commutative Noetherian ring, this gives a particularly nice understanding of all injective modules, described in.
- A "'Gorenstein ring "'is a commutative Noetherian ring such that each Cohen Macaulay.
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