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# Article

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Keywords:
kappa-slender module; $k$-coordinatewise slender; $k$-tailwise slender; $k$-cslender; $k$-tslender; slender module; $k$-hmodule; the Hom functor; infinite products; filtered products; infinite coproducts; filtered products; non-measurable cardinal; torsion theory
Summary:
For an arbitrary infinite cardinal $\kappa$, we define classes of $\kappa$-cslender and $\kappa$-tslender modules as well as related classes of $\kappa$-hmodules and initiate a study of these classes.
References:
[1] Dimitric, R.: Slenderness in Abelian Categories. Abelian Group Theory: Proceedings of the Conference at Honolulu, Hawaii, Lect. Notes Math. 1006, 1006, 1983, 375-383, Berlin: Springer Verlag, MR 0722633
[2] Dimitric, R.: Slenderness. Vol. I. Abelian Categories. 2018, Cambridge Tracts in Mathematics No. 215. Cambridge: Cambridge University Press, ISBN: 9781108474429. MR 3930609
[3] Dimitric, R.: Slenderness. Vol. II. Generalizations. Dualizations. 2021, Cambridge Tracts in Mathematics. Cambridge: Cambridge University Press, MR 3930609
[4] Fuchs, L.: Abelian Groups. 1958, Budapest: Publishing House of the Hungarian Academy of Science, Reprinted by New York: Pergamon Press (1960).. MR 0106942 | Zbl 0091.02704
[5] Hrbacek, K., Jech, T.: Introduction to Set Theory (3rd edition, revised and expanded). 1999, New York -- Basel: Marcel Dekker, MR 1697766
[6] Łoś, J.: Linear equations and pure subgroups. Bull. Acad. Polon. Sci, 7, 1959, 13-18, MR 0103922
[7] Stenström, B.: Rings of Quotients. An Introduction to Methods of Ring Theory. 1975, Berlin, Heidelberg, New York: Springer-Verlag, MR 0389953

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