Categorical properties of generalized σ-derivations on modules

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.

Keywords:

• Generalized σ-derivations
• modules
• path algebras
• quivers
• semi-monoidal categories

2020 Mathematics Subject Classification:

• 16W25
• 18A25

Acknowledgments

The authors would like to thank the referee, whose valuable comments and advice improved much of the paper.

Disclosure statement

The authors report there are no competing interests to declare.