Right-left symmetry of \(aR\oplus bR=(a+b)R\) in regular rings (Q1295647)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Right-left symmetry of \(aR\oplus bR=(a+b)R\) in regular rings |
scientific article; zbMATH DE number 1308266
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Right-left symmetry of \(aR\oplus bR=(a+b)R\) in regular rings |
scientific article; zbMATH DE number 1308266 |
Statements
Right-left symmetry of \(aR\oplus bR=(a+b)R\) in regular rings (English)
0 references
2 November 1999
0 references
The somewhat surprising symmetry condition of the title is proved, in the following generality: If \(R\) is a ring, \(a,b\in R\), and \(a+b\) is a von Neumann regular element of \(R\), then \(aR\oplus bR=(a+b)R\) if and only if \(Ra\oplus Rb=R(a+b)\).
0 references
von Neumann regular rings
0 references
