Bi-derivation on Polynomial Ring

Selvi Diana Dwi Rinanda; Fitriani Fitriani; Ahmad Faisol

doi:10.24198/jmi.v22.n1.70123.1-18

Bi-derivation on Polynomial Ring

Selvi Diana Dwi Rinanda, Fitriani Fitriani, Ahmad Faisol

Abstract

Derivations and their generalizations play an important role in understanding the structure of rings. One natural extension of derivations is the notion of a biderivation, which is a bi-additive mapping satisfying derivation-type identities in each argument. In this paper, we investigate biderivations on polynomial rings. Several examples of biderivations are constructed and some of their fundamental properties are established. In particular, we study the relationship between biderivations defined on a ring $R$ and those induced on the polynomial ring $R[x]$. The obtained results provide additional insight into the behavior of biderivations under polynomial ring extensions.

Keywords

ring; polynomial ring; derivation; biderivation

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References

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DOI: https://doi.org/10.24198/jmi.v22.n1.70123.1-18