A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS

Year 2020, Volume: 28 Issue: 28, 75 - 97, 14.07.2020

Maryam Hamıdızadeh Ebrahim Hashemı Armando Reyes

https://doi.org/10.24330/ieja.768178

Cited By: 7

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

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