(Generalized) tilting modules with respect to the category σ[M]. Issue 12 (2nd December 2021)

• Record Type: Journal Article
• Authors: Abbaszade, M.; Mousavi, S. Sh.
• Is Part Of: Communications in algebra. Volume 49:Issue 12(2021)
• Page Start: 5354
• Page End: 5366
• Publication Date: 2021-12-02
• Subjects: (Generalized) M-tilting module -- partial M-tilting module -- σ-projective (σ-global) dimension -- tilting module in -- σ[M]; 16D90; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.1944174
• Languages: English
• ISSNs: 0092-7872

Abstract

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.