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Iterated skew polynomial rings of Krull dimension two. (English) Zbl 0809.16031
Let \(A\) be a finitely generated algebra over an algebraically closed field \(k\). Let \(\alpha\) be a \(k\)-automorphism and let \(R\) denote the iterated skew polynomial ring \(A[y; \alpha][x; \alpha^{-1}, \delta]\). The main intent of this article is to show that if \(A\) is \(\alpha\)-simple and a principal ideal domain and if \(X\) is a finitely generated right \(R\)-module such that both \(X_ x\) and \(X_ y\) have finite length, then \(X\) has finite length. This eliminates the need in earlier work of the author to assume that all finite dimensional modules were semisimple.

MSC:
16S36 Ordinary and skew polynomial rings and semigroup rings
16P60 Chain conditions on annihilators and summands: Goldie-type conditions
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16P10 Finite rings and finite-dimensional associative algebras
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References:
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