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In a previous paper, the author together with prof. dr. Finston constructed aclass of UFDs A_{n,m} where n,m\in \N^*. These rings are all stably equivalent(A_{n,m}[T]\cong A_{p,q}[T] for all n,m,p,q) but are only isomorphic themselvesif (n,m)=(p,q). These examples are the first UFD examples over acharacteristically closed field satisfying this behavior. In this paper, wedescribe the methods used in this article, and show that they are very general,enabling the reader to construct many more such examples, based on the sameprinciples.

On the methods to construct UFD counterexamples to a cancellation problem