… 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 …

… (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 …

… finite asymptotic dimension is weakly coherent. In particular, there is a large collection of
R[Γ ]-modules of finite homological dimension when R is a finite-dimensional regular ring. This …

… 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 …

… 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 …

… coherence disappears for higher rank modules and we must rely on cardinality conditions to
give estimates of the dimensions… dimension two, what conditions are forced on the base ring …

… ) global dimension of slightly (m, n)-coherent rings are investigated. … coherent rings, these
homological dimensions share many nice properties as the classical homological dimensions…