Simple derivations in two variables. Issue 9 (2nd September 2019)

• Record Type: Journal Article
• Authors: Yan, Dan
• Is Part Of: Communications in algebra. Volume 47:Issue 9(2019)
• Page Start: 3881
• Page End: 3888
• Publication Date: 2019-09-02
• Subjects: Simple derivations -- polynomial rings; 13N15 -- 13C99; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1572165
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: In this article, we study theK -derivation of the form: D = y ∂ x + ( a 2 y 2 + a 1 ( x ) y + a 0 ( x ) ) ∂ y with a 2 ∈ K and a 1 ( x ), a 0 ( x ) ∈ K [ x ] . We show that D is simple if and only if a 0 ( x ) ∈ K * and deg a 1 ( x ) ≥ 1 .