noetherian ring उदाहरण वाक्य

उदाहरण वाक्य

1. Most of them coincide with the Krull dimension for Noetherian rings, but can differ for non-Noetherian rings.
2. Most of them coincide with the Krull dimension for Noetherian rings, but can differ for non-Noetherian rings.
3. Over a Noetherian ring, every injective module is the direct sum of ( uniquely determined ) indecomposable injective modules.
4. I would also endorse keeping " Noetherian rings "-how many people have a mathematical concept named after them?
5. Therefore, for noncommutative Noetherian rings, these two versions coincide and one is justified in talking about the global dimension.
6. In fact, this can be generalized to right noetherian rings; this result is known as Levitzky's theorem.
7. Since PID's are Noetherian rings, this can be seen as a manifestation of the Lasker-Noether theorem.
8. All Dedekind domains of characteristic 0 and all local Noetherian rings of dimension at most 1 are J-2 rings.
9. By Hilbert's basis theorem and some elementary properties of Noetherian rings, every affine or projective coordinate ring is Noetherian.
10. A ring is left Noetherian if and only if all its left ideals are finitely generated; analogously for right Noetherian rings.