Communications of the
Korean Mathematical Society CKMS

We investigate the relation between the notion of $e$-exactness, recently introduced by Akray and Zebary, and some functors naturally related to it, such as the functor $P\colon\Mod R\to \Spec(\Mod R)$, where $\Spec(\Mod R)$ denotes the spectral category of $\Mod R$, and the localization functor with respect to the singular torsion theory.

Keywords: Relative exactness of sequences, spectral category

MSC numbers: Primary 16E30

Supported by: The second author is supported by Ministero dell’Istruzione, dell’Universit? e della Ricerca(Progetto di ricerca di rilevante interesse nazionale “Categories, Algebras: Ring-Theoretical and Homological Approaches (CARTHA)”) and Dipartimento di Matematica “Tullio Levi-Civita” of Universit? di Padova (Research program DOR1828909 “Anelli e categorie dimoduli”).