Modules commuting (via Hom) with some limits

• Autorzy: Robert El Bashir , Tomáš Kepka
• Języki publikacji: EN

Abstrakty

EN

For every module M we have a natural monomorphism
 $Φ: ∐_{i ∈ I} Hom _R (A_i,M) → Hom _R (∏_{i ∈I} A_i, M)$
and we focus attention on the case when Φ is also an epimorphism. The corresponding modules M depend on thickness of the cardinal number card(I). Some other limits are also considered.

Kategorie tematyczne

• 16B99: None of the above, but in this section
• 16E30: Homological functors on modules (Tor, Ext, etc.)
• 18A35: Categories admitting limits (complete categories), functors preserving limits, completions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 155
• Numer: 3
• Strony: 271-292

Daty

wydano

1998

otrzymano

1996-11-14

poprawiono

1997-09-23

Twórcy

autor

Robert El Bashir

• KA MFF UK, Sokolovská 83, 186 00 Praha 8 - Karlín, Czech Republic

autor

Tomáš Kepka

• KA MFF UK, Sokolovská 83, 186 00 Praha 8 - Karlín, Czech Republic

Bibliografia

• [1] D. Allouch, Modules maigres, thèse, Montpellier, 1969/70.
• [2] L. Bican, J. Jirásko, T. Kepka and B. Torrecillas, Modules and their extensions I. (Purities), Publ. Dept. Math. M93001 (1993), Faculty of Civil Engin., Czech Techn. Univ., Prague.
• [3] R. Dimitrić, Slender modules over domains, Comm. Algebra 11 (1983), 1685-1700.
• [4] R. Dimitrić, Slenderness in abelian categories, in: Abelian Group Theory, Lecture Notes in Math. 1006, Springer, 1983, 375-383.
• [5] K. Eda, A Boolean power and a direct product of abelian groups, Tsukuba J. Math. 6 (1982), 187-193.
• [6] K. Eda, On a Boolean power of a torsion free Abelian group, J. Algebra 82 (1983), 84-93.
• [7] K. Eda, Slender modules, endo-slender abelian groups and large cardinals, Fund. Math. 135 (1990), 5-24.
• [8] A. Ehrenfeucht and J. Łoś, Sur les produits cartésiens des groupes cycliques infinies, Bull. Acad. Polon. Sci. Sér. Astronom. Phys. Sci. Math. 2 (1954), 261-263.
• [9] P. Eklof and A. Mekkler, Almost Free Modules, North-Holland, 1990.
• [10] R. El Bashir and T. Kepka, On when small semiprime rings are slender, Comm. Algebra 24 (1996), 1575-1580.
• [11] R. El Bashir and T. Kepka, Notes on slender prime rings, Comment. Math. Univ. Carolin. 37 (1996), 419-422.
• [12] R. El Bashir, T. Kepka and P. Němec, Modules commuting (via Hom) with some colimits, preprint.
• [13] L. Fuchs, Abelian Groups, Pergamon Press, 1960.
• [14] L. Fuchs, Infinite Abelian Groups, Vol. I, Academic Press, 1970.
• [15] L. Fuchs, Infinite Abelian Groups, Vol. II, Academic Press, 1973.
• [16] L. Fuchs and L. Salce, Modules over Valuation Domains, M. Dekker, 1985.
• [17] G. Heinlein, Vollreflexive Ringe und schlanke Moduln, Dissertation, Erlangen, 1971.
• [18] L. Henkin, A problem on inverse mapping systems, Proc. Amer. Math. Soc. 1 (1950), 224-225.
• [19] A. Kanamori, The Higher Infinite, Springer, 1994.
• [20] S. Koppelberg, Handbook of Boolean Algebras, Vol. I, North-Holland, 1989.
• [21] E. Lady, Slender rings and modules, Pacific J. Math. 49 (1973), 397-406.
• [22] A. Mader, Groups and modules that are slender as modules over their endomorphism rings, in: Abelian Groups and Modules, CISM Courses and Lectures 287, Springer, 1984, 315-327.
• [23] G. de Marco and A. Orsatti, Complete linear topologies on abelian groups, Sympos. Math. 13 (1974), 153-161.
• [24] R. Nunke, Slender groups, Acta Sci. Math. (Szeged) 23 (1962), 67-73.
• [25] A. Pultr and V. Trnková, Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories, North-Holland, 1980.
• [26] L. Salce, Moduli slender su anelli di Dedekind, Ann. Univ. Ferrara Sez. VII Sci. Math. 20 (1975), 59-63.
• [27] E. Sąsiada, Proof that every countable and reduced torsion-free abelian group is slender, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 7 (1959), 143-144.
• [28] J. Trlifaj, Similarities and differences between abelian groups and modules over non-perfect rings, in: Contemp. Math. 171 Amer. Math. Soc., 1994, 397-406.
• [29] R. Wisbauer, Grundlagen der Modul und Ringtheorie, R. Fisher, 1988.