What is "bimodule"

n. (context mathematics English) An abelian group that is both a left and a right module, such that the left and right multiplications are compatible

In abstract algebra, a bimodule is an abelian group that is both a left and a right module, such that the left and right multiplications are compatible. Besides appearing naturally in many parts of mathematics, bimodules play a clarifying role, in the sense that many of the relationships between left and right modules become simpler when they are expressed in terms of bimodules.