Morita equivalence

In <a href="/facts/Abstract_algebra/YNNE1CNz">abstract algebra</a>, Morita equivalence is a relationship defined between <a href="/facts/Ring_(mathematics)/JnCUXz63">rings</a> that preserves many <a href="/facts/Ring_theory/VW6svEFe">ring-theoretic</a> properties. More precisely, two rings R, S are Morita equivalent (denoted by 
 
 
 
 R
 ≈
 S
 
 
 {\displaystyle R\approx S}
 
) if their <a href="/facts/Category_of_modules/AnnF9JKf">categories of modules</a> are <a href="/facts/Additive_category/TWUcFazd">additively</a> <a href="/facts/Equivalence_of_categories/k6uzqAcy">equivalent</a> (denoted by

R
          
        
        M
        ≈

S
 
 
 M
 
 
 {\displaystyle {}_{R}M\approx {}_{S}M}
 
). It is named after Japanese mathematician <a href="/facts/Kiiti_Morita/zm4KvU1s">Kiiti Morita</a> who defined equivalence and a similar notion of <a href="/facts/Duality_(mathematics)/8jGuyQIU">duality</a> in 1958.

Morita equivalence open-in-new

Morita equivalence