ASSOCIATED PRIMES OVER ORE EXTENSION RINGS

The study of the prime ideals in Ore extension rings R[x,σ,δ] has attracted a lot of attention in recent years and has proven to be a challenging undertaking ([5], [7], [12], et al.). The present article makes a contribution to this study for the associated prime ideals. More precisely, we aim to describe how the associated primes of an R-module MR behave under passage to the polynomial module M[x] over an Ore extension R[x,σ,δ]. If we impose natural σ-compatibility and δ-compatibility assumptions on the module MR (see Sec. 2 below), we can describe all associated primes of the R[x,σ,δ]-module M[x] in terms of the associated primes of MR in a very straightforward way. This result generalizes the author's recent work [1] on skew polynomial rings.