On the regular elements in Zn

Authors : Osama ALKAM

Pages : 31-39

View : 19 | Download : 3

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :All rings are assumed to be finite commutative with identity element. An element a \in R is called a regular element if there exists b \in R such that a=a2b, the element b is called a von Neumann inverse for a. A characterization is given for regular elements and their inverses in Zn, the ring of integers modulo n. The arithmetic function Vinsert ignore into journalissuearticles values(n);, which counts the regular elements in Zn is studied. The relations between Vinsert ignore into journalissuearticles values(n); and Euler`s phi-function j insert ignore into journalissuearticles values(n); are explored.
Keywords : Regular elements, Eular`s phi function, von Neumann regular rings