Exceptional and complementable units in rings
Year: 2026
Type: article
Abstract: A unit u in a ring R is called exceptional if $$1-u$$ 1 - u is also a unit. Such units have been previously studied from a Number Theory perspective. In this paper, we investigate exceptional units from the standpoint of Ring Theory, with particular emphasis on matrix rings, where several characterizations are provided. We define and explore a special subclass of exceptional units, termed complementable units. An exceptional unit u is called complementable if $$u(1-u)=1$$ u ( 1 - u ) = 1 . We determine the residue class rings that contain complementable units and identify such units in certain matrix rings.
Source: Arabian Journal of Mathematics
Author: Grigore Călugăreanu
Institution: Babeș-Bolyai University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7161742880