Local ring：abstract algebra
abstract algebra
Local ring
https://en.wikipedia.org
In mathematics, more specifically in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called local ...
Section 10.18 (07BH)
https://stacks.math.columbia.e
A local ring is a ring with exactly one maximal ideal. If R is a local ring, then the maximal ideal is often denoted -mathfrak m_ R and the field R/-mathfrak m ...
local ring in nLab
https://ncatlab.org
An important example of a local ring in algebraic geometry is R = k [ ϵ ] / ϵ 2 R = k[-epsilon]/-epsilon^2 . This ring is known as the ring of dual numbers.
Local Ring
https://mathworld.wolfram.com
A local ring is a ring R that contains a single maximal ideal. In this case, the Jacobson radical equals this maximal ideal. One property of a local ring R ...
Regular local ring
https://en.wikipedia.org
A regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal is equal to its Krull dimension.
CHARACTERIZATION OF LOCAL RINGS
https://projecteuclid.org
A ring with identity is said to be a local ring if the sum of any two non-units is a non-unit or equivalently if the ring has a unique maximal right ideal. Most ...
(PDF) On Local Rings
https://www.researchgate.net
A ring R is called local ring if it has exactly one maximal ideal. In this paper, we introduce some characterization and basic properties of ...