Turkish Journal of Mathematics
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=a^2b, the element b is called a von Neumann inverse for a. A characterization is given for regular elements and their inverses in Z_n, the ring of integers modulo n. The arithmetic function V(n), which counts the regular elements in Z_n is studied. The relations between V(n) and Euler's phi-function \varphi (n) are explored.
DOI
-
Keywords
Regular elements, Eular's phi-function, von Neumann regular rings
First Page
31
Last Page
39
Recommended Citation
ALKAM, O, & OSBA, E. A (2008). On the regular elements in Z_n. Turkish Journal of Mathematics 32 (1): 31-39. https://doi.org/-
