On the candidate counter-example in the cancellation problem for affine spaces

Details On the candidate counter-example in the cancellation problem for affine spaces On the candidate counter-example in the cancellation problem for affine spaces

2012-01-20

arxiv.org/abs/1201.4198v4

Mathematics

Commutative Algebra

8 pages, I add one more section and Theorem 2.1 is a little revised

Scientific paper

The Cancellation Problem is the following : Let $ k $ be a field of characteristic zero and let $n \in \mathbb{N}$ with $n \geq 2$. If $R[Y] \cong_k k[X_1, ..., X_{n}]$ as a $k$-algebra, where $Y, X_1, ..., X_{n}$ are indeterminates, then $R \cong_k k[X_1, ..., X_{n-1}]$. In this paper, it is shown that the candidate (or possible) counterexample of the above problem in $n=5$ conjectured by van den Essen, Arno and P. van Rossum {\bf [1]} is not the Case. So the Cancellation Problem is still open for $n \geq 3$.

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