… The class of left N0-coherent rings includes all rings with countably generated left ideals ([5,
lemma 1]), and all left coherent rings, ie for instance left semi-hereditary rings and rings of …

… Chapter 3 and section 1 in Chapter 7 develop many of the tools of modern research in
commutative algebra such as several homological dimensions, Fitting invariants, Euler …

… Section 3 explores descent of regularity, primarily in case the ring is coherent. Related to
coherent regularity, this section also explores the behavior of the weak dimensions of the rings …

… between homological dimensions of Noetherian rings … the ring while restricting the mo dules
to be finitely presented. For this it is convenient to introduce homological dimensions of rings …

… coherent rings give a more complete picture and unify various results from [II09]. Ultimately,
given a (left) coherent ring … generated whenever R is a coherent ring. We reprove the needed …

… ring if and only if R is a Noetherian ring and G is a finitely generated group. Motivated by this
result we ask when is RG a coherent ring… weak dimension of RG when RG is a coherent ring…

… give homological descriptions of the Gorenstein dimensions over arbitrary associative
rings. … However, over a right coherent ring there is a connection between Gorenstein flat left …

… all rings R have an identity element and all R-modules are unitary. For background in ring
… [l] or Lambek C71; results on homological dimensions can be found in Cartan and Eilenberg …

… (or injective) dimensions of simple modules [11… coherent ring or a right semi-artinian ring,
then we may compute the (weak) global dimension of R using just the homological dimensions …

… these weak dimensions, provided that R is a stably coherent ring of finite weak dimension.
As … We next explore the homological properties of R(x) and R(x) as exhibited in the behaviour …