What is the meaning of Local?

From or in a nearby location.

Connected directly to a particular computer, processor, etc.; able to be accessed offline.

Having limited scope (either lexical or dynamic); only accessible within a certain portion of a program.

Applying to or satisfied by substructures understood as "near points;" in particular:

1. Satisfied by at least one open neighborhood of every point.

   Satisfied by at least one open neighborhood of every point.

   Satisfied by arbitrarily small open neighborhoods of every point.

   Satisfied by every finitely generated subgroup.

   Detectable from the behavior of substructures understood to be "near points;" in particular:

   1. Such that the following conditions are equivalent: (1) ${\displaystyle P}$ holds for ${\displaystyle R}$ (${\displaystyle M}$); (2) ${\displaystyle P}$ holds for the localization ${\displaystyle R_{\mathfrak {p}}}$ (${\displaystyle M_{\mathfrak {p}}}$) for all prime ideals ${\displaystyle {\mathfrak {p}}}$ of ${\displaystyle R}$; (3) ${\displaystyle P}$ holds for the localization ${\displaystyle R_{\mathfrak {m}}}$ (${\displaystyle M_{\mathfrak {m}}}$) for all maximal ideals ${\displaystyle {\mathfrak {m}}}$ of ${\displaystyle R}$.

      Such that the following conditions are equivalent: (1) ${\displaystyle P}$ holds for ${\displaystyle R}$ (${\displaystyle M}$); (2) ${\displaystyle P}$ holds for the localization ${\displaystyle R_{\mathfrak {p}}}$ (${\displaystyle M_{\mathfrak {p}}}$) for all prime ideals ${\displaystyle {\mathfrak {p}}}$ of ${\displaystyle R}$; (3) ${\displaystyle P}$ holds for the localization ${\displaystyle R_{\mathfrak {m}}}$ (${\displaystyle M_{\mathfrak {m}}}$) for all maximal ideals ${\displaystyle {\mathfrak {m}}}$ of ${\displaystyle R}$.

      Detectable from the behavior of the normalizers of the nontrivial p-subgroups.

      Having a unique maximal (left) ideal.

      Of or pertaining to a restricted part of an organism.

      Descended from an indigenous population.

      A person who lives near a given place.

      A branch of a nationwide organization such as a trade union.

      Clipping of local train.

      One's nearest or regularly frequented public house or bar.

      A locally scoped identifier.

      An item of news relating to the place where the newspaper is published.

      Clipping of local anesthetic.

      An independent trader who acts for themselves rather than on behalf of investors.

      A Twitter user who is not a part of Stan Twitter.

      In the local area; within a city, state, country, etc.

      Alternative form of llocal

      local

      property, premises; business, storefront

      local (people, as opposed to foreigners)

      local

      premises; rooms

      local

      local

      room

      local

      premises; rooms

      local

      local

      room

      local

      premises, rooms

      site

      place, location

      local

      local

      premises, rooms

      store or other retail unit in a shopping center

      Source: wiktionary.org