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).


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
Full Text: DOI Euclid


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