… The first systematic study of the category mod-A of right modules over a ring A was done, I …
think about rings and modules functorially. Rather than solve problems in-ring theory, category …

… R (always associative with 1) we denote by Mod R th category of all left R-modules and by
mod … the fact that a ring R is left coherent if and only if mod R is an abelian category and for the …

… coherent, we identify C0 with the finitely presented modules, but we do not know what it is in
general. We recall that a thick subcategory of a triangulated category … R is a coherent ring. A …

… Abstract For a left coherent ring A with every left ideal having a … category of left A-modules
is compactly generated by the bounded derived category of finitely presented left A-modules (…

… Localizing at the Serre subcategory of finitely presented R-modules of finite length, one
obtains a category equivalent to the category of finitely presented modules over the ring RrkŽ ., …

… This paper also yields a module version of the bijection between the set of localizing … Let
R be a commutative ring. We denote by Mod R the category of R-modules and by mod R the full …

… When R is a quasi-Frobenius or Gorenstein ring, these triangulated categories agree with
… the usual stable module category. Our stable module categories are homotopy categories of …

… that if R is a left coherent ring and S any ring and an (R,S)-… FP-injective resolution, then a
module A in mod R satisfying Ext R … is a left coherent ring and S is a right coherent ring and R ω …

… modules, and Fn,d the class of (n, d)-flat right R-modules. In this paper, we prove that if R is a
left n-coherent ring … if Extm+k(M, N) = 0 for all left R-modules M, N and all k ≥ −1, if and only …

… a ring by considering a given set of conditions on the modules it admits and at other
times we will consider a ring of a certain type to see what structure is forced on its modules. …