… In addition, we give two examples, which show how to compute the relative homological
groups over a coherent ring. In Section 3, we establish some isomorphism theorems about …

… coherent sheaf over a … -coherent R-modules, where R is a representation by rings of a quiver
Q, and we prove the existence of a flat cover and a cotorsion envelope for quasi-coherent R-…

… ring R is coherent on both sides, we show that silp R + silp Rop = spli R + spli Rop. In particular,
if R is a commutative coherent ring, … In the special case of a left ℵ0-coherent ring, we aim …

… von Neumann regular rings and (m,n)-coherent rings. Some known results are extended. …
Throughout this article, R is an associative ring with identity and all modules are unitary. For an …

… presheaves of homotopy groups are quasi-coherent sheaves for … ring A, the cyclotomic
trace map is a map of symmetric ring spectra. In particular, the induced map of homotopy groups …

… the relative K-theory is identified with relative topological cyclic … Given a ring R, we can form
both its Hochschild homology … any connective spectrum whose homology groups are finitely …

… and some relative modules and … coherent ring then RH is a left n-coherent ring. Moreover,
if RG is a separable extension over RH; the skew group ring RG is a left n-coherent ring …

… We define the topological Hochschild homology R-module TH H^*(A; M) of A with coef…
motopy and homology groups. Again, classical Hochschild homology and cohomology groups are …

… We will call a quasicoherent graded algebra B over X Noetherian if the graded ring B.U / is
… Then we will use the finite homological dimension property of locally projective graded B-…

… of some homological properties of modules and rings with respect to … rings which are coherent
relative to certain matrices. Given a β × α matrix A over R, we say R is left coherent relative …