Toen: The homotopy theory of dg-cats and derived Morita theory. File Toen web publ mapdgcat.pdf.
Chapter 6 of Anderson and Fuller, in Homol alg folder
Chapter 7 of Lam: Lectures on modules and rings. In Homol alg folder
Title: Flat Model Structures for Nonunital Algebras and Higher K-Theory. Authors: S. Estrada and P.A. Guil-Asensio. We prove the existence of a Quillen Flat Model Structure in the category of unbounded complexes of h-unitary modules over a nonunital ring (or a -algebra, with a field). This model structure provides a natural framework where a Morita-invariant homological algebra for these nonunital rings. http://arxiv.org/abs/0906.4735
Morita theory: Borceaux vol 2 pp 180. Two rings are Morita equivalent if their categories of right modules are equivalent. Can define Morita equivalence more generally for algebraic theories other than rings. If R is commutative with unit, then R and and the ring of nxn square matrices over R are Morita equiv. Two things with unit which are Morita equiv have isomorphic centres. Two commutative rings with unit are Morita equiv iff they are isomorphic.
See also Weibel for Morita equiv.
nLab page on Morita theory