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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Original Russian Text © A.V. Cherednikova, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 1, pp. 60–76.
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Cherednikova, A.V. Rings of quasi-endomorphisms of some direct sums of torsion-free Abelian groups. Russ Math. 61, 53–68 (2017). https://doi.org/10.3103/S1066369X17010078
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DOI: https://doi.org/10.3103/S1066369X17010078