Let R be an hereditary Noetherian prime ring (or, HNP-ring, for short), and let S= R [x; σ] be a
skew polynomial ring over R with σ being an automorphism on R. The aim of the paper is to
describe completely the structure of right projective ideals of R [x; σ] where R is an HNP-ring
and to obtain that any right projective ideal of S is of the form X𝔟 [x; σ], where X is an
invertible ideal of S and 𝔟 is a σ-invariant eventually idempotent ideal of R.

This talk is mainly based on a joint work, with the same title, by E. Akalan, P. Aydogdu, H.
Marubayashi, B. Saraç and A. Ueda. Let R be an hereditary Noetherian prime ring (or, HNP
ring, for short), and let S= R [x; σ] be a skew polynomial ring over R with σ being an
automorphism on R. Our first goal is to characterize maximal right and left v-ideals (or
equivalently ideals which are maximal amongst right or left projective ideals) of S as the
same set consisting of certain type of ideals that are either idempotent or invertible. Next, we …