For a ring R, we prove that all left R-modules have weak injective covers and weak injective
preenvelopes. Then we characterize the right weak injective dimension of modules in terms …

If R is left noetherian and M is a left R-module, then we can construct a complex called an
injective resolvent of M using injective precovers. Likewise, if R is left coherent and M is a …

In Section 1 of this paper, we investigate the finitely presented dimension of an essential
extension for a module, and obtain results concerning an essential extension of a torsion …

Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree
dimension of finitely generated R-modules. For any n≧0, we prove that R is a Gorenstein …

We prove that (a) if R is a commutative coherent ring, the weak global dimension of R equals
the supremum of the flat (or (FP–) injective) dimensions of the simple R-modules;(b) if R is …

Throughout this note, R stands for a ring with identity and all modules are unital modules. In
this note, for a given module M, we say that M has dominant dimension at least ny written …

Introduction. For a ring S, let FPD (S) denote the right finitistic projective dimension of S, that
isr the supremum of the finite projective dimensions of right S-modules. If S is a projective …

The flat dimensions of injective modules Page 1 manuscripta math. 78, 165- 177 (1993)
manuscripta mathematica Spfinger-Verlag 1~3 THE FLAT DIMENSIONS OF INJECTIVE …

In this paper, we study the existence of L⊥-envelopes, L-envelopes, D⊥-envelopes, D-
covers, and L-covers where L and D denote the classes of modules of injective and …

Then 6 (R) is also equal to sup {id (M)(M is a cocyclic left R module}. Ot course the
homological invariant 6 (R) is< gld (R). For a commutative ring R it is easy to prove that 6 …