Rings of quasi-endomorphisms of some direct sums of torsion-free Abelian groups |
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Authors: | A V Cherednikova |
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Institution: | 1.Kostroma State University,Kostroma,Russia |
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Abstract: | We consider a representation of quasi-endomorphisms of Abelian torsion-free groups of rank 4 bymatrices of order 4 over the field of rational numbers Q. We obtain a classification for quasi-endomorphism rings of Abelian torsion-free groups of rank 4 quasi-decomposable into a direct sum of groups A 1, A 2 of rank 1 and strongly indecomposable group B of rank 2 such that quasi-homomorphism groups Q ? Hom(A i , B) and Q ? Hom(B, A i ) for any i = 1, 2 have rank 1 or are zero. Moreover, for algebras from the classification we present necessary and sufficient conditions for their realization as quasi-endomorphism rings of these groups. |
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