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Displaying similar documents to “A Note on Additive Groups of Some Specific Associative Rings”

Square subgroups of rank two abelian groups

A. M. Aghdam, A. Najafizadeh (2009)

Colloquium Mathematicae

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Let G be an abelian group and ◻ G its square subgroup as defined in the introduction. We show that the square subgroup of a non-homogeneous and indecomposable torsion-free group G of rank two is a pure subgroup of G and that G/◻ G is a nil group.

Units in group rings of crystallographic groups

Karel Dekimpe (2003)

Fundamenta Mathematicae

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In [3], the authors initiated a technique of using affine representations to study the groups of units of integral group rings of crystallographic groups. In this paper, we use this approach for some special classes of crystallographic groups. For a first class of groups we obtain a normal complement for the group inside the group of normalized units. For a second class of groups we show that the Zassenhaus conjectures ZC1 and ZC3 are valid. This generalizes the results known for the...

Generalized morphisms of abelian m-ary groups

Alexander M. Gal'mak (2001)

Discussiones Mathematicae - General Algebra and Applications

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We prove that the set of all n-ary endomorphisms of an abelian m-ary group forms an (m,n)-ring.

Butler groups splitting over a base element

Clorinda De Vivo, Claudia Metelli (2007)

Colloquium Mathematicae

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We characterize a particular kind of decomposition of a Butler group that is the general case for Butler B(1)-groups; and exhibit a decomposition of a B(2)-group which is not of that kind.