Quasi duo skew polynomial rings

André Leroy (1) , Jerzy Matczuk (2) , Edmund Puczylowski (2)

1 LML - Laboratoire de Mathématiques de Lens
2 Institute of Mathematics [Warsaw]

A characterization of right (left) quasi-duo skew polynomial rings of endomorphism type and skew Laurent polynomial rings are given. In particular, it is shown that (1) the polynomial ring R[x] is right quasi-duo iff R[x] is commutative modulo its Jacobson radical iff R[x] is left quasi-duo, (2) the skew Laurent polynomial ring is right quasi-duo iff it is left quasi-duo. These extend some known results concerning a description of quasi-duo polynomial rings and give a partial answer to the question posed by Lam and Dugas whether right quasi-duo rings are left quasi-duo.

Mots clés: Quasi duo rings; skew polynomial rings

Domaines: Anneaux et algèbres [math.RA]

André Leroy, Jerzy Matczuk, Edmund Puczylowski. Quasi duo skew polynomial rings. Journal of Pure and Applied Algebra, 2008, 212 (8), pp.1951-1959. ⟨hal-00416136⟩