Journals / International Electronic Journal of Algebra / 2020 / Cilt: 28 - Sayı: 28
A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS
- Pages
- 75–97
- DOI
- —
Abstract
For a skew PBW extension over a right duo compatible ring, we characterize several kinds of their elements such as units, idempotent, von Neumann regular, $\pi$-regular and the clean elements. As a consequence of our treatment, we extend several results in the literature for Ore extensions and commutative rings. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$