Editing Glossary of ring theory (section)

== L ==
{{glossary}}

{{term|1=local}}
{{defn|no=1|1=A ring with a unique maximal left ideal is a [[local ring]]. These rings also have a unique maximal right ideal, and the left and the right unique maximal ideals coincide. Certain commutative rings can be embedded in local rings via [[localization of a ring|localization]] at a [[prime ideal]].}}
{{defn|no=2|1=A [[localization of a ring]] : For commutative rings, a technique to turn a given set of elements of a ring into units. It is named ''Localization'' because it can be used to make any given ring into a ''local'' ring. To localize a ring ''R'', take a multiplicatively closed subset ''S'' that contains no [[zero divisor]]s, and formally define their multiplicative inverses, which are then added into ''R''. Localization in noncommutative rings is more complicated, and has been in defined several different ways.}}

{{glossary end}}