Ring elements as sums of units

• Autorzy: Charles Lanski , Attila Maróti
• Języki publikacji: EN

Abstrakty

EN

In an Artinian ring R every element of R can be expressed as the sum of two units if and only if R/J(R) does not contain a summand isomorphic to the field with two elements. This result is used to describe those finite rings R for which Γ(R) contains a Hamiltonian cycle where Γ(R) is the (simple) graph defined on the elements of R with an edge between vertices r and s if and only if r - s is invertible. It is also shown that for an Artinian ring R the number of connected components of the graph Γ(R) is a power of 2.

Słowa kluczowe

EN

Artinian rings; Units; Hamiltonian cycle

Kategorie tematyczne

• 16P20: Artinian rings and modules
• 05C45: Eulerian and Hamiltonian graphs
• 16U60: Units, groups of units

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 3
• Strony: 395-399

Daty

wydano

2009-09-01

online

2009-08-12

Twórcy

autor

Charles Lanski

• University of Southern California

autor

Attila Maróti

• MTA Alfréd Rényi Institute of Mathematics

Bibliografia

• [1] Jacobson N., Structure of rings, American Mathematical Society Colloquium Publications, 1956, 37
• [2] Lovász L., Combinatorial problems and exercises, North-Holland, Amsterdam, 1979
• [3] Lucchini A., Maróti A., Some results and questions related to the generating graph of a finite group, Proceedings of the Ischia Group Theory Conference 2008 (to appear)

Identyfikatory

DOI

10.2478/s11533-009-0024-5