1. Categorical properties of generalized σ-derivations on modules.
- Author
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Adrabi, Abderrahim, Bennis, Driss, and Fahid, Brahim
- Subjects
COMMUTATIVE algebra ,COMMUTATIVE rings ,TENSOR products ,ALGEBRA ,CATEGORIES (Mathematics) ,ACYCLIC model ,MORPHISMS (Mathematics) - Abstract
Let S be an algebra over a commutative ring R, and let σ be an automorphism on S. In this paper, we investigate the notion of generalized σ-derivations on modules, which is an extension of generalized derivations on modules introduced by Nakajima. Namely, we study homological properties of generalized σ-derivations. Also, we equip the category of functors that send S/R-modules to R-modules of generalized σ-derivations with a tensor product. We show this category is semi-monoidal. As an application, we characterize when a generalized derivation on a path algebra of an acyclic quiver is a generalized inner derivation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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