On products of self-small abelian groups
Keywords:
Self-small abelian group.Abstract
An abelian group A is called self-small if direct sums of copies of A commute with the covariant Hom(A;-) functor. The paper presents an elementary example of a non-self-small countable product of self-small abelian groups without non-zero homomorphisms between different ones. A criterion of self-smallness of a finite product of modules is given.
Mathematics Subject Classification (2010): 16D10, 16S50, 16D70.
References
Albrecht, U., Breaz, S., Wickless, W., The finite quasi-Baer property, J. Algebra, 293(2005), 1-16.
Albrecht, U., Breaz, S., Wickless, W., Self-small Abelian groups, Bull. Aust. Math. Soc., 80(2009), no. 2, 205-216.
Albrecht, U., Breaz, S., Wickless, W., Purity and self-small groups, Commun. Algebra, 35(2007), no. 11, 3789-3807.
Arnold, D.M., Murley, C.E., Abelian groups A such that Hom(A;) preserves direct sums of copies of A, Pacific Journal of Mathematics, 56(1975), no. 1, 7-20.
Breaz, S., Schultz, P., Dualities for Self-small Groups, Proc. A.M.S., 140(2012), no. 1, 69-82.
Breaz, S., _Zemlicka, J., When every self-small module is finitely generated, J. Algebra, 315(2007), 885-893.
Calugareanu, G., Breaz, S., Modoi, C., Pelea, C., V_alcan, D., Exercises in abelian group theory, Kluwer Texts in the Mathematical Sciences, Kluwer, Dordrecht, 2003.
Colpi, R., Menini, C., On the structure of *-modules, J. Algebra, 158(1993), 400-419.
Fuchs, L., Infinite Abelian Groups, Vol. I, Academic Press, New York and London, 1970.
Gomez Pardo, J.L., Militaru, G., Nastasescu, C., When is HOM(M;) equal to Hom(M;) in the category R gr?, Comm. Algebra, 22(1994), 3171-3181.
Zemlicka, J., Classes of dually slender modules, Proceedings of the Algebra Symposium, Cluj, 2005, Editura Efes, Cluj-Napoca, 2006, 129-137.
Zemlicka, J., When products of self-small modules are self-small, Commun. Algebra, 36(2008), no. 7, 2570-2576.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
