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Kappa-slender modules. (English) Zbl 1475.16012

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.

MSC:

16D80 Other classes of modules and ideals in associative algebras
18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
03C20 Ultraproducts and related constructions
03E10 Ordinal and cardinal numbers
20K25 Direct sums, direct products, etc. for abelian groups
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References:

[1] R. Dimitric: Slenderness in Abelian Categories. In: Göbel R., Lady L., Mader A.: Abelian Group Theory: Proceedings of the Conference at Honolulu, Hawaii, Lect. Notes Math. 1006. Berlin: Springer Verlag (1983) 375-383.
[2] R. Dimitric: Slenderness. Vol. I. Abelian Categories. Cambridge Tracts in Mathematics No. 215. Cambridge: Cambridge University Press (2018). ISBN: 9781108474429
[3] R. Dimitric: Slenderness. Vol. II. Generalizations. Dualizations. Cambridge Tracts in Mathematics. Cambridge: Cambridge University Press (2021).
[4] L. Fuchs: Abelian Groups. Budapest: Publishing House of the Hungarian Academy of Science (1958). Reprinted by New York: Pergamon Press (1960). · Zbl 0091.02704
[5] K. Hrbacek , T. Jech: Introduction to Set Theory (3rd edition, revised and expanded). New York - Basel: Marcel Dekker (1999). · Zbl 1045.03521
[6] J. Loś: Linear equations and pure subgroups. Bull. Acad. Polon. Sci 7 (1959) 13-18. · Zbl 0083.25101
[7] B. Stenström: Rings of Quotients. An Introduction to Methods of Ring Theory. Berlin, Heidelberg, New York: Springer-Verlag (1975). · Zbl 0296.16001
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