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Ring elements as sums of units

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Lanski C., Maróti A.

Open Mathematics

2009

tom 7

nr 3

395-399

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.

Addendum to “Ring elements as sums of units”

100%

Lanski C., Maróti A.

Open Mathematics

2013

tom 11

nr 5

984-984

We give a comment to Theorem 1.1 published in our paper “Ring elements as sums of units” [Cent. Eur. J. Math., 2009, 7(3), 395–399].

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2 Open Mathematics

2 Lanski C.

2 Maróti A.

1 2013

1 2009

Wyniki wyszukiwania

Ring elements as sums of units

Addendum to “Ring elements as sums of units”