Osama ALKAM

85117

On the regular elements in Zn

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 V(n), which counts the regular elements in Zn is studied. The relations between V(n) and Euler's phi-function j (n) are explored.

Anahtar Kelimeler:

Regular elements, Eular's phi-function, von Neumann regular rings

On the regular elements in Zn

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 V(n), which counts the regular elements in Zn is studied. The relations between V(n) and Euler's phi-function j (n) are explored.

Keywords:

Regular elements, Eular's phi-function, von Neumann regular rings,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

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