(Generalized) tilting modules with respect to the category σ[M]. Issue 12 (2nd December 2021) - Abbaszade, M.; Mousavi, S. Sh.
Abstract: In this article, we provide a new generalization of tilting modules, named (generalized) tilting modules with respect to σ[ M ], or simply (generalized) M -tilting modules and then characterize (generalized) M -tilting modules using the projective dimension in σ [ M ], under certain conditions. We discuss the relation between this new generalization and the Wisbauer's generalization and study some of its properties. Also, when M is a Σ 1 σ -module we introduce and study "partial M -tilting modules" as a generalized form of partial tilting modules.