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Onα-almost Artinian modules

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Davoudian M., Halali A., Shirali N.

Open Mathematics

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2016

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tom 14

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nr 1

404-413

EN

In this article we introduce and study the concept of α-almost Artinian modules. We show that each α-almost Artinian module M is almost Artinian (i.e., every proper homomorphic image of M is Artinian), where α ∈ {0,1}. Using this concept we extend some of the basic results of almost Artinian modules to α-almost Artinian modules. Moreover we introduce and study the concept of α-Krull modules. We observe that if M is an α-Krull module then the Krull dimension of M is either α or α + 1.

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Ring elements as sums of units

100%

Lanski C., Maróti A.

Open Mathematics

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2009

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tom 7

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nr 3

395-399

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.

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Addendum to “Ring elements as sums of units”

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Lanski C., Maróti A.

Open Mathematics

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2013

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tom 11

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nr 5

984-984

EN

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].

Ograniczanie wyników

3 Open Mathematics

2 Lanski C.

2 Maróti A.

1 Davoudian M.

1 Halali A.

1 Shirali N.

1 2016

1 2013

1 2009

Onα-almost Artinian modules

Ring elements as sums of units

Addendum to “Ring elements as sums of units”