Regular elements in ring [tough one]
Source: IMS 2008
May 10, 2008
group theoryabstract algebraRing Theorysuperior algebraregular element
Problem Statement
Prove that there does not exist a ring with exactly 5 regular elements.
( is called a regular element if ax \equal{} 0 or xa \equal{} 0 implies x \equal{} 0.)
A ring is not necessarily commutative, does not necessarily contain unity element, or is not necessarily finite.