… dimension, called the cotorsion dimension, for modules and rings. The relations between the
cotorsion dimension and other dimensions … of cotorsion modules contains all pure-injective (…

… cotorsion (The converses do not hold in general; however, flat cotorsion modules over left
coherent rings are pure-injective, [81]). The class of all pure-injective, and cotorsion, modules …

… = 0 (the condition Ext(T,Q) = 0 is vacuous, since Q is injective), and it is in this sense that
the concept of cotorsion is dual to that of torsion. Cotorsion Abelian groups were so named by …

… We characterize rings over which every cotorsion module is pure injective (Xu rings) in …
case of flat modules. Along with pseudoflat modules we introduce quasiflat modules, which arise …

… Thus, as a corollary of Theorem 2.8, we obtain that if U is a cotilting Rmodule, then the
cotorsion theory generated by U is perfect; in particular CogenU is a cover class. We could get the …

… examples of cotorsion theories … 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 …

… are connected by the following result: A torsion-free module with no preprojective direct
summand is pure injective if and only if it is cotorsion. A pure injective module Mcan also be put …

… The class of cotorsion modules contains all pure injective (… a dimension, called the S-cotorsion
dimension, for modules and rings… the S-cotorsion dimension and the other dimensions are …

… by a Σ -pure-injective cotilting module if and only if its heart is a … -pure-injective cotilting module
of injective dimension at most … torsion pairs induced by Σ -pure-injective cotilting modules. …

… -module C is called cotorsion if for any flat right R -module biF… cotorsion envelopes that are
analogous to those on injective … which every cotorsion right R -module is 𝒜-injective, where 𝒜 …