… weak injective if Ext R 1 ( N , E ) = 0 for every super finitely presented R-module N; the weak
injective dimension … Now, we will give a new characterization of the weak injective modules. …

… the homological dimensions of R in terms of P1-injective modules. In particular, we prove
the following formula for the weak global dimension and the global dimension of a ring R: …

… modules, respectively, it follows at once that these classes are equal exactly if the weak
global dimension of the ring does not exceed 1. This means that the ring (that must be noetherian…

… aspects of modules with finite n-weak injective and n-weak flat dimensions. We let W I k n ( …
of left and right modules with n-weak injective dimension and n-weak flat dimension at most k, …

… -injective in case all the simple modules are reflexive. Here, we exhibit an 8-dimensional
algebra which is not self-injective, … are reflexive by the much weaker assumption that all simple …

… weak limit of a sequence of \(W^1_q\)-homeomorphisms with finite distortion to be almost
everywhere injective … , in every dimension \(n\ge 3\), a Lipschitz mapping of finite distortion such …

… provides weak reflections for the full subcategory of approximately injective objects. For this
… We prove that finite-dimensional Banach spaces are approximately small wrt isometries and …

… via their finite-dimensional representations. In contrast with the elementary matricial description
of finite-dimensional C ⁎ -algebras, … We show next that a weaker statement always hold. …

… We will need information on the Hausdorff dimension of images of spheres embedded in
Rn. The following is a special case of such a result in [9] for Bessel potential functions, which …

… 5, asserts that any right E-ring is finite dimensional (ie, satisfies acc = the acc on direct sums
… noetherian, or (weaker) that J(Q)/J(Q)² has finite length [eg, when J(Q)² = 0 (Corollary 9.6)]. …