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.
@article{bwmeta1.element.doi-10_2478_s11533-009-0024-5,
author = {Charles Lanski and Attila Mar\'oti},
title = {Ring elements as sums of units},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {395-399},
zbl = {1185.16026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0024-5}
}
Charles Lanski; Attila Maróti. Ring elements as sums of units. Open Mathematics, Tome 7 (2009) pp. 395-399. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0024-5/
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