Coherent Rings and Homologically Finite Subcategories

摘要

Introduction. For an arbitrary ring R (always associative with 1) we denote by Modi? the category of all left R-modules and by mod R the full subcategory of Mod R with objects the finitely presented modules. Here we recall that a module M in Mod R is said to be finitely presented if there is an exact sequence F→F'→M→0 with F and F finitely generated free modules. By a subcategory of mod R we always understand a full subcategory closed under isomorphisms. By a functor from a subcategory ? of mod R to the category Ab of abelian groups we will understand an additive functor (covariant or contravariant).