Year: 2015
Type: preprint
Abstract: The notion of clean rings and 2-good rings have many variations, and have been widely studied. We provide a few results about two new variations of these concepts and discuss the theory that ties these variations to objects and properties of interest to noncommutative algebraists. A ring is called nil-good if each element in the ring is the sum of a nilpotent element and either a unit or zero. We establish that the ring of endomorphisms of a module over a division is nil-good, as well as some basic consequences. We then define a new property we call nil-good clean, the condition that an element of a ring is the sum of a nilpotent, an idempotent, and a unit. We explore the interplay between these properties and the notion of clean rings.
Source: arXiv (Cornell University)
Authors: Gorman, Alexi Block, Shiao, Wing Yan
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2213548877