Ore Extensions and V -domains
نویسندگان
چکیده
We give necessary and sufficient conditions for a skew polynomial ring K[t; σ, δ] 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× n matrices over K are (σ, δ)-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 open question or answering it in the affirmative for the ring K[t; σ, δ].
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