Abstract
An example is given of a self-injective commutative von Neumann regular algebra over the rationals, that is not elementarily equivalent to a function ring.
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Carson, A.B. Self-injective regular algebras and function rings. Algebra Universalis 29, 449–454 (1992). https://doi.org/10.1007/BF01212444
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DOI: https://doi.org/10.1007/BF01212444