ASSOCIATED PRIMES OVER ORE EXTENSION RINGS

The study of the prime ideals in Ore extension rings R[x, sigma, delta] 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 M-R behave under passage to the polynomial module M[x] over an Ore extension R[x, sigma, delta]. If we impose natural sigma-compatibility and delta-compatibility assumptions on the module M-R (see Sec. 2 below), we can describe all associated primes of the R[x, sigma, delta]-module M[x] in terms of the associated primes of M-R in a very straightforward way. This result generalizes the author's recent work [1] on skew polynomial rings.