Resolutions in cotorsion theories

Abstract

We consider the λ- (μ-) and λ̄- (μ̄-) dimensions of modules taken under a cotorsion theory (F, C) satisfying the Hereditary Condition, and establish some inequalities between the dimensions of the modules of a short exact sequence, not necessarily Hom (F, -) exact. We investigate the question of whether the property of having a (special) F- or C-resolution of length n is resolving, closed under extensions or coresolving and establish some inequalities connecting the λ- (μ-) and λ̄- (μ̄-) dimensions of modules in a short exact sequence. © 2010 American Institute of Physics.