Projective ideals of skew polynomial rings over HNP rings

ABSTRACT

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.

KEYWORDS:

• Hereditary Noetherian prime ring
• projective ideal
• skew polynomial ring

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16A05
• 16D40
• 16A12