## On 2-stably isomorphic four-dimensional affine domains.(English)Zbl 1448.13014

The author gives examples of four-dimensional semi-normal domains $$A$$ and $$B$$ which are finitely generated over the field $$\mathbb C$$ (or $$\mathbb R$$) such that $$A[X,Y]=B[X,Y]$$ but $$A[X]\not\cong B[X].$$ The method is purely algebraic. The first examples of this type was given by Z. Jelonek [Math. Ann. 344, No. 4, 769–778 (2009; Zbl 1178.14060)], (the examples of Z. Jelonek are smooth and they have dimension ten).

### MSC:

 13B25 Polynomials over commutative rings 13F20 Polynomial rings and ideals; rings of integer-valued polynomials 13F45 Seminormal rings 14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)

Zbl 1178.14060
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### References:

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