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Preprint Number 90

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90. Sonia L'Innocente, Mike Prest
Ring of definable scalars of Verma modules

Submission date: 17 October 2007.


Let M be a Verma module over the Lie algebra, sl(2,k), of trace zero 2x2 matrices over the algebraically closed field k. We show that the ring of definable scalars of M is a von Neumann regular ring. We also describe the Ziegler closure of M. The proofs make use of ideas from the model theory of modules.

Mathematics Subject Classification: 03C60

Keywords and phrases: Verma module, ring of definable scalars, Ziegler closure

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