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. (C) 1998 Academic Press.