Morita equivalence

In abstract algebra, Morita equivalence is a relationship defined between rings that preserves many ring-theoretic properties. More precisely, two rings R, S are Morita equivalent (denoted by ${\displaystyle R\approx S}$) if their categories of modules are additively equivalent (denoted by ${\displaystyle {}_{R}M\approx {}_{S}M}$). It is named after Japanese mathematician Kiiti Morita who defined equivalence and a similar notion of duality in 1958.