Abstract
This chapter discusses the global dimensions of ore extensions and Weyl algebras. If R is a ring and D is a derivation of R, and if S = R[t, D] is the ore extension of R with respect to D, that is, S is additively the group of polynomials in an indeterminate t with multiplication subject to tr = rt + D(r) for all r in R, then an extension of D to a derivation of S by setting D(t) = 0 for all elements s of S leads to the result ts = st + D(s). If R is a commutative noetherian ring, and if M → 0 is a left A1R-module that is finitely generated as a left R-module, then M is an abelian torsion group.
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