local ring in a sentence

Examples

1. He proved the Cohen structure theorem for complete Noetherian local rings.
2. The paper showed that a germs of holomorphic functions, local rings, and differential forms.
3. The dual numbers form a local ring since there is a unique maximal ideal.
4. The product of the local rings of a commutative ring is a faithfully flat module.
5. A colorful truck with a loudspeaker announcing a bullfight at a local ring passed by.
6. Local rings play a major role in valuation theory.
7. Certain commutative rings can be embedded in local rings via localization at a prime ideal.
8. In the local ring case, it does matter.
9. Serre proved this for all regular local rings.
10. This ring is a 2-dimensional Noetherian regular local ring, and in particular a unique factorization domain.