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Quasiendomorphism algebras of some quasidecomposable rank 4 torsion-free abelian groups

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Abstract

We classify the quasiendomorphism algebras of rank 4 torsion-free abelian groups quasidecomposable as the direct sum of strongly indecomposable rank 2 groups.

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References

  1. Beaumont R. A. and Pierce R. S., “Torsion free groups of rank two,” Mem. Amer. Math. Soc., 38, 1–41 (1961).

    MathSciNet  MATH  Google Scholar 

  2. Cherednikova A. V., “Quasiendomorphism rings of almost completely decomposable torsion-free abelian groups of rank 3,” in: Abelian Groups and Modules [Russian]. Vol. 13–14, Tomsk Univ., Tomsk, 1996, pp. 237–242.

    MATH  Google Scholar 

  3. Cherednikova A. V., “Rings of quasiendomorphisms of quasidecomposable torsion-free abelian groups of rank 3,” in: Abelian Groups and Modules [Russian], Tomsk Univ., Tomsk, 1996, No. 13–14, pp. 224–236.

    MATH  Google Scholar 

  4. Cherednikova A. V., “Rings of quasi-endomorphisms of strongly indecomposable torsion-free Abelian groups of rank 3,” Math. Notes, 63, No. 5, 670–678 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  5. Faticoni T. G., Direct Sum Decompositions of Torsion-Free Finite Rank Groups, Chapman and Hall/CRC, Boca Raton and New York (2007).

    Book  MATH  Google Scholar 

  6. Cherednikova A. V., “Rings of quasi-endomorphisms of strongly indecomposable torsion-free abelian groups of rank 4 with pseudosocles of rank 3,” J. Math. Sci. (New York), 177, No. 6, 942–946 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  7. Cherednikova A. V., “Quasi-endomorphism rings of strongly indecomposable torsion-free abelian groups of rank 4 with pseudosocles of rank 1,” J. Math. Sci. (New York), 197, No. 6, 703–707 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  8. Cherednikova A. V., “Quasi-endomorphism rings of almost completely decomposable torsion-free abelian groups of rank 4 with zero Jacobson radical,” J. Math. Sci. (New York), 197, No. 5, 698–702 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  9. Cherednikova A. V., “Quasi-endomorphism rings of almost completely decomposable torsion-free Abelian groups of rank 4 that do not coincide with their pseudo-socles,” Math. Notes, 97, No. 4, 621–631 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  10. Warfield R., “Homomorphisms and duality for torsion free groups,” Math. Z., Bd 107, 189–200 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  11. Fuchs L., Infinite Abelian Groups. Vol. 2, Academic Press, New York and London (1973).

    MATH  Google Scholar 

  12. Pierce R. S., Associative Algebras, Springer-Verlag, New York, Heidelberg, and Berlin (1982).

    Book  MATH  Google Scholar 

  13. MacLane S., Homology, Springer-Verlag, Berlin etc. (1963).

    Book  MATH  Google Scholar 

  14. Reid J. D., “On the ring of quasi-endomorphism of a torsion-free group,” in: Topics in Abelian Groups, Scott, Foresman and Co., Chicago; Ill., 1963, pp. 51–68.

    Google Scholar 

  15. Arnold D. M., Finite Rank Torsion Free Abelian Groups and Rings, Springer-Verlag, Berlin and Heidelberg (1982) (Lect. Notes Math.; V. 931).

    Book  MATH  Google Scholar 

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Correspondence to A. V. Cherednikova.

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Original Russian Text Copyright © 2016 Cherednikova A.V.

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Cherednikova, A.V. Quasiendomorphism algebras of some quasidecomposable rank 4 torsion-free abelian groups. Sib Math J 57, 1088–1099 (2016). https://doi.org/10.1134/S0037446616060161

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