Differential Operators on Noncommutative Rings

摘要

Let k be a commutative ring and R an associative k-algebra. In this paper wedefine the ring D(R) of k-linear differential operators on R. In case R is commutative this, of course, coincides with Grothendieck's definition (G). Given left R-modules L, N we define the differential operators Diff(L,N) from L to N as the differential part of the R-biomodule Homk(L,N). Thus our main definition is the differential part Mdiff of an arbitrary R-bimodule M.