Normal Quadratics in Ore Extensions, Quantum Planes, and Quantized Weyl Algebras

Details Normal Quadratics in Ore Extensions, Quantum Planes, and Quantized Weyl Algebras Normal Quadratics in Ore Extensions, Quantum Planes, and Quantized Weyl Algebras

2005-08-25

arxiv.org/abs/math/0508513v2

2009 Acta Appl. Math. 108 (1), 73-81

Mathematics

Rings and Algebras

Scientific paper

Let R be a Noetherian domain and let ({\sigma}, {\delta}) be a quasi-derivation of R such that {\sigma} is an automorphism. There is an induced quasi-derivation on the classical quotient ring Q of R. Suppose F = t^2 - v is normal in the Ore extension R[t; {\sigma}, {\delta}] where v {\epsilon} R. We show F is prime in R[t; {\sigma}, {\delta}] if and only if F is irreducible in Q[t; {\sigma}, {\delta}] if and only if there does not exist w {\epsilon} Q such that v = {\sigma} (w)w - {\delta} (w). We apply this result to classify prime quadratic forms in quantum planes and quantized Weyl algebras.

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