On the subgroups of completely decomposable torsion-free groups that are ideals in every ring

Aghdam, A. M.; Karimi, Fatemeh; Najafizadeh, Alireza

doi:10.5817/am2012-2-107

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2016

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“…Remark 2.6. Notice that the above theorem is the partial answer to the question posed at the end of [2]. The answer is only partial, because we restrict our consideration to the class of associative rings.…”

Section: S -Groupsmentioning

confidence: 99%

See 1 more Smart Citation

A Note on Additive Groups of Some Specific Associative Rings

Woronowicz

2016

Annales Mathematicae Silesianae

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Almost complete description of abelian groups (A, +, 0) such that every associative ring R with the additive group A satisfies the condition: every subgroup of A is an ideal of R, is given. Some new results for SR-groups in the case of associative rings are also achieved. The characterization of abelian torsion-free groups of rank one and their direct sums which are not nil-groups is complemented using only elementary methods.

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Section: S -Groupsmentioning

confidence: 99%

“…SGI-groups are related to SR-groups studied, for example by A.M. Aghdam, F. Karimi and A. Najafizdeh in [2]. An SR-group is an abelian group whose all subgroups are subrings of any (not necessarily associative) ring defined on it.…”

Section: Introductionmentioning

confidence: 99%

A Note on Additive Groups of Some Specific Associative Rings

Woronowicz

2016

Annales Mathematicae Silesianae

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show abstract

On the subgroups of completely decomposable torsion-free groups that are ideals in every ring

Cited by 1 publication

References 2 publications

A Note on Additive Groups of Some Specific Associative Rings

A Note on Additive Groups of Some Specific Associative Rings

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