local
Language: English
Part of speech: adj
Pronunciation: ipa: /ˈləʊ.kl̩/
enpr: lōk′əl
ipa: /ˈloʊ.kl̩/
rhymes: -əʊkəl
Forms: form: more local
form: most local
Etymology: From Middle English local, from Late Latin locālis (“belonging to a place”), possibly also via Old French local; ultimately from Latin locus (“a place”).
The ring-theoretic senses derive from Krull, who first referred to Noetherian commutative rings with a unique maximal ideal as "Stellenring" (Stellen (“place”) + ring) in 1938. The term was inspired by algebraic geometry, where local rings encode information about the behavior of curves (surfaces, etc.) at points; hence, describe "local" behavior.
Senses: examples: text: We prefer local produce.
text: Not unnaturally, “Auntie” took this communication in bad part.[…]Next day she[…]tried to recover her ward by the hair of the head. Then, thwarted, the wretched creature went to the police for help; she was versed in the law, and perhaps had spared no pains to keep on good terms with the local constabulary.
ref: 1918, W[illiam] B[abington] Maxwell, chapter XLIV, in The Mirror and the Lamp, Indianapolis, Ind.: The Bobbs-Merrill Company, →OCLC, page 361:
text: A farmer could place an order for a new tractor part by text message and pay for it by mobile money-transfer. A supplier many miles away would then take the part to the local matternet station for airborne dispatch via drone.
ref: 2012 December 1, “An internet of airborne things”, in The Economist, volume 405, number 8813, page 3 (Technology Quarterly):
holonyms: statal
national
federal
unional
supranational
global
glosses: From or in a nearby location.
examples: text: local disk drive
text: local file
text: The panel shows both local and remote sites.
topics: computing
engineering
mathematics
natural-sciences
physical-sciences
sciences
antonyms: remote
glosses: Connected directly to a particular computer, processor, etc.; able to be accessed offline.
raw_tags: of a resource
topics: computing
engineering
mathematics
natural-sciences
physical-sciences
sciences
antonyms: global
glosses: Having limited scope (either lexical or dynamic); only accessible within a certain portion of a program.
raw_tags: of a variable or identifier
examples: text: A Hausdorff space satisfying local compactness need not be (globally) compact!
topics: mathematics
sciences
topology
glosses: Applying to or satisfied by substructures understood as "near points;" in particular:
Satisfied by at least one open neighborhood of every point.
raw_tags: of a condition or property
topics: mathematics
sciences
topology
glosses: Applying to or satisfied by substructures understood as "near points;" in particular:
Satisfied by arbitrarily small open neighborhoods of every point.
raw_tags: of a condition or property
topics: group-theory
mathematics
sciences
glosses: Applying to or satisfied by substructures understood as "near points;" in particular:
Satisfied by every finitely generated subgroup.
raw_tags: of a property of an infinite group
of a condition or property
examples: text: Flatness is a local property.
topics: algebra
algebraic-geometry
geometry
mathematics
sciences
glosses: Detectable from the behavior of substructures understood to be "near points;" in particular:
Such that the following conditions are equivalent: (1) P holds for R (M); (2) P holds for the localization R_p (M_p) for all prime ideals p of R; (3) P holds for the localization R_m (M_m) for all maximal ideals m of R.
raw_tags: of a property P of a ring R (or an R-module M)
of a condition or property
topics: group-theory
mathematics
sciences
glosses: Detectable from the behavior of substructures understood to be "near points;" in particular:
Detectable from the behavior of the normalizers of the nontrivial p-subgroups.
raw_tags: of a property of a finite group
of a condition or property
topics: algebra
mathematics
sciences
glosses: Having a unique maximal (left) ideal.
raw_tags: of a ring
examples: text: local lesion
text: The patient didn't want to be sedated, so we applied only local anesthesia.
topics: medicine
sciences
synonyms: topical
glosses: Of or pertaining to a restricted part of an organism.
examples: text: Hawaiian Pidgin is spoken by the local population.
glosses: Descended from an indigenous population.