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Everything about Local ring
(Mathematical) ring with a unique maximal ideal
In mathematics, more specifically in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defined on algebraic varieties or manifolds, or of algebraic number fields examined at a particular place, or prime. Local algebra is the branch of commutative algebra that studies commutative local rings and their modules. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Local ringA 5-minute orientation
- Skim a recent paper: Engineering a local acid-like environment in alkaline medium for efficient hydrogen evolution reactionInfluential work since 2022
- Pick up a classic book: IEEE standard for information technologyThe most-reprinted book on the subject
- Read the landmark paper: On the associated graded ring of a local Cohen-Macaulay ringCited 102 times
- Go sideways: Glossary of ring theoryA closely related topic
- Go sideways: Krull dimensionA closely related topic
📖 Definitions
Noun A commutative ring with a unique maximal ideal, or a noncommutative ring with a unique maximal left ideal or (equivalently) a unique maximal right ideal.
Noun The non-routing segment of a token ring network.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
On the associated graded ring of a local Cohen-Macaulay ring
The Poincaréseries of a local ring
Asymmetric ring current at twilight local time
On the deviations of a local ring.
Modules with semi-local endomorphism ring
The local cohomology of the Jacobian ring
Valuations Associated with a Local Ring (I)
Valuations Associated with a Local Ring (II)
🆕 Influential since 2022
Engineering a local acid-like environment in alkaline medium for efficient hydrogen evolution reaction
Engineering the Local Microenvironment over Bi Nanosheets for Highly Selective Electrocatalytic Conversion of CO 2 to HCOOH in Strong Acid
Engineering the Local Atomic Environments of Indium Single‐Atom Catalysts for Efficient Electrochemical Production of Hydrogen Peroxide
Tailoring a local acid-like microenvironment for efficient neutral hydrogen evolution
📚 Books worth reading
IEEE standard for information technologyInstitute of Electrical and Electronics Engineers · 1991
Local algebraJean-Pierre Serre · 1965
Localization in Noetherian ringsA. V. Jategaonkar · 1986
Inside the Token-RingJ. Scott Haugdahl · 1986
Dualisierende Komplexe in der lokalen Algebra und Buchsbaum--RingePeter Schenzel · 1982
Token ring networksJohn R. Abrahams · 1991
Localization and sheavesP. Jara, Jara Pascual · 1995
Lecture Notes on Local RingsBirger Iversen · 2014
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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