Ore extensions and V-domains

André Leroy (1) , Surender Jain (2) , Tsit Lam (3)

1 LML - Laboratoire de Mathématiques de Lens
2 Department of Mathematics, Ohio University, Athens
3 Department of Mathematics [Berkeley]

We give necessary and sufficient conditions for a skew polynomial ring K[t;\sigma, \delta] over a division ring K to be a left V-domain. In particular, when this ring admits a unique simple left module, the conditions obtained include: 1) all polynomials are Wedderburn, 2) all n by n matrices over K are (\sigma,\delta)-similar. We also provide necessary and sufficient conditions for this ring to be both left and right V-domain. These results, that are indeed motivated by a long-standing open question whether a left V-domain is a right V-domain, provide clues towards finding a possible counterexample to this question or answering it in the affirmative for the ring K[t;\sigma,\delta].

Mots clés: V-domain; PCI domain; Ore extensions; injective modules

Domaines: Anneaux et algèbres [math.RA]

André Leroy, Surender Jain, Tsit Lam. Ore extensions and V-domains. Communications in Contemporary Mathematics, 2009, 480, pp.249-261. ⟨hal-00416137⟩