Abstract
It is wellknown that the Jacobson radical of a unital ring R is the largest superfluous right ideal of R. While a simple example shows this to be false for nonunital rings, it is shown that the result remains valid in the absence of a unit provided the notion of "superfluous" is taken relative to all regular right ideals. The purpose of this note is to provide a proof for this littleknown fact.
Original language  English 

Pages (fromto)  47404742 
Number of pages  3 
Journal  Communications in Algebra 
Volume  47 
Issue number  11 
Early online date  13 Apr 2019 
DOIs  
Publication status  Published  2019 
ASJC Scopus subject areas
 Mathematics(all)
 Algebra and Number Theory
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Thomas Huettemann
 School of Mathematics and Physics  Senior Lecturer
 Mathematical Sciences Research Centre
Person: Academic