Dimitric, Radoslav Kappa-slender modules. (English) Zbl 1475.16012 Commun. Math. 28, No. 1, 1-12 (2020). 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 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 PDFBibTeX XMLCite \textit{R. Dimitric}, Commun. Math. 28, No. 1, 1--12 (2020; Zbl 1475.16012) Full Text: DOI arXiv 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.