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Research Article

(Generalized) tilting modules with respect to the category σ[M]

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Pages 5354-5366 | Received 08 Sep 2020, Accepted 10 Jun 2021, Published online: 17 Aug 2021
 

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 Σ1σ-module we introduce and study “partial M-tilting modules” as a generalized form of partial tilting modules.

2020 Mathematics Subject Classification:

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