Krull Dimension of Generalized Weyl Algebras and Iterated Skew Polynomial Rings: Commutative Coefficients

Many rings that have enjoyed growing interest in recent years, e.g., quantum enveloping algebras, quantum matrices, certain Witten-algebras,…,can be presented as generalized Weyl algebras. In the paper we develop techniques for calculating dimensions, here mainly the Krull dimension in the sense of Rentschler–Gabriel, of such generalized Weyl algebras and specify the results for some popular algebras including those mentioned above.