Is there an example of commutative von Neumann regular ring which has more than 2 prime ideals?
Matrix rings are not commutative so I couldn't find any, please help.
2026-04-04 04:37:15.1775277435
Commutative von Neumann regular ring with more than two prime ideals.
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It is well-known that the quotient of a commutative ring by is nilradical is absolutely flat if and only if every prime ideal is maximal(Bourbaki, Commutative Algebra, Ch. II Localisation, §4, exercise 16 d) – in other words, a reduced ring is absolutely flat if and only if it has Krull dimension $0$.
Therefore a product of more than $2$ copies of a field provides such an example.