Abstract
In this paper, we consider multilinear maps of an Abelian group into itself (n-multiplications) and their properties. We obtain equivalent conditions for an Abelian group to be an E-group in terms of n-multiplications. A correlation between properties of n-multiplications on the Abelian group at various n is found.
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References
D. M. Arnold, Finite Rank Torsion Free Abelian Groups and Rings, Lect. Notes Math., Vol. 931, Springer, Berlin (1982).
L. Fuchs, Infinite Abelian Groups, Vols. 1, 2, Academic Press, New York (1970, 1973).
P. A. Krylov, A. V. Mikhalev, and A. A. Tuganbaev, Endomorphism Rings of Abelian Groups, Dordrecht, Kluwer Academic (2003).
P. Schultz, “The endomorphism ring of the additive group of a ring,” J. Aust. Math. Soc., 15, 60–69 (1973).
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 5, pp. 55–63, 2019.
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Karpov, O.A. Correlation between E-Groups and Properties of n-Multiplications on Abelian Groups. J Math Sci 259, 420–426 (2021). https://doi.org/10.1007/s10958-021-05630-w
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DOI: https://doi.org/10.1007/s10958-021-05630-w