Finite length and pure-injective modules over a ring of differential operators

[摘要] Let k be an algebraically closed field of characteristic zero, O-n = k[[x(1),...,x(n)]] the ring of formal power series over k, and D-n the ring of differential operators over O-n. Suppose that rho is a prime ideal of O-n of height n - 1; i.e., A = O-n/rho is a curve. We prove that every indecomposable finite length module over D-n with support on rho is uniserial with isomorphic or alternating composition factors. For the ring D(A) of differential operators over A we also classify indecomposable pure-injective modules and show that the Cantor-Bendixson rank of the Ziegler spectrum over D(A) is equal to 2. (C) 2000 Academic Press.

[发布日期] 2000-09-15