Linkage of modules

It is shown that the notion of linkage of algebraic varieties, introduced by Peskine and Szpiro, can be generalized to finitely generated modules over non-commutative noetherian semiperfect rings. Besides greater generality, the module-theoretic approach brings about new invariants of linkage and yields improved results and simpler proofs even in the traditional settings of commutative algebraic geometry and local algebra. Connections with Auslander–Reiten sequences, singularity theory, derived categories, local cohomology, Buchsbaum modules, and maximal Cohen–Macaulay approximations are discussed.