- International Electronic Journal of Algebra
- Volume:28 Issue:28
- A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS
A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS
Authors : Maryam HAMIDIZADEH, Ebrahim HASHEMI, Armando REYES
Pages : 75-97
Doi:10.24330/ieja.768178
View : 16 | Download : 15
Publication Date : 2020-07-14
Article Type : Research Paper
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. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$Keywords : Right duo ring, skew PBW extension, idempotent element, unit element, von Neumann regular element, clean element