Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
395-399
Opis fizyczny
Daty
wydano
2009-09-01
online
2009-08-12
Twórcy
autor
- University of Southern California, clanski@usc.edu
autor
- MTA Alfréd Rényi Institute of Mathematics, maroti@renyi.hu
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)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0024-5