Modules commuting (via Hom) with some colimits

Robert El Bashir; Tomáš Kepka; Petr Němec

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 4, page 891-905
  • ISSN: 0011-4642

Abstract

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For every module M we have a natural monomorphism Ψ : ∐ i ∈ I H o m R ( M , A i ) → H o m R M , ∐ i ∈ I A i and we focus our attention on the case when Ψ is also an epimorphism. Some other colimits are also considered.

How to cite

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Bashir, Robert El, Kepka, Tomáš, and Němec, Petr. "Modules commuting (via Hom) with some colimits." Czechoslovak Mathematical Journal 53.4 (2003): 891-905. <http://eudml.org/doc/30822>.

@article{Bashir2003,
abstract = {For every module $M$ we have a natural monomorphism \[ \Psi :\coprod \_\{i\in I\}\mathop \{\mathrm \{H\}om\}\nolimits \_R(M,A\_i)\rightarrow \mathop \{\mathrm \{H\}om\}\nolimits \_R\biggl (M,\coprod \_\{i\in I\}A\_i\biggr ) \] and we focus our attention on the case when $\Psi $ is also an epimorphism. Some other colimits are also considered.},
author = {Bashir, Robert El, Kepka, Tomáš, Němec, Petr},
journal = {Czechoslovak Mathematical Journal},
keywords = {module; colimit; finitely presented module; colimits; finitely presented modules},
language = {eng},
number = {4},
pages = {891-905},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Modules commuting (via Hom) with some colimits},
url = {http://eudml.org/doc/30822},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Bashir, Robert El
AU - Kepka, Tomáš
AU - Němec, Petr
TI - Modules commuting (via Hom) with some colimits
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 4
SP - 891
EP - 905
AB - For every module $M$ we have a natural monomorphism \[ \Psi :\coprod _{i\in I}\mathop {\mathrm {H}om}\nolimits _R(M,A_i)\rightarrow \mathop {\mathrm {H}om}\nolimits _R\biggl (M,\coprod _{i\in I}A_i\biggr ) \] and we focus our attention on the case when $\Psi $ is also an epimorphism. Some other colimits are also considered.
LA - eng
KW - module; colimit; finitely presented module; colimits; finitely presented modules
UR - http://eudml.org/doc/30822
ER -

References

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  1. Algebraic K -Theory, W. A. Benjamin, New York, 1968. (1968) Zbl0174.30302MR0249491
  2. On the structure of * -modules, J. Algebra 158 (1993), 400–419. (1993) MR1226797
  3. 10.1080/00927879408825060, Comm. Algebra 22 (1994), 3985–3995. (1994) MR1280103DOI10.1080/00927879408825060
  4. Dually slender modules and steady rings, Forum Math. 9 (1997), 61–74. (1997) MR1426454
  5. Almost Free Modules, North-Holland, New York, 1990. (1990) MR1055083
  6. Modules commuting (via H o m ) with some limits, Fund. Math. 155 (1998), 271–292. (1998) MR1607449
  7. Abelian Categories, , New York, 1964. (1964) Zbl0121.02103
  8. Modules over Valuation Domains, Marcel Dekker, New York, 1985. (1985) MR0786121
  9. ∑ -compact modules and steady rings, Ph.D.  Thesis, Charles University, Prague, 1997. (1997) 
  10. When is H O M R ( M , - ) equal to H o m R ( M , - ) in the category R - g r ? Comm, Algebra 22 (1994), 3171–3181. (1994) MR1272380
  11. 10.1216/RMJ-1972-2-2-235, Rocky Mountain  J.  Math. 2 (1972), 235–237. (1972) MR0294388DOI10.1216/RMJ-1972-2-2-235
  12. ∩ -compact modules, Comment. Math. Univ. Carolin. 36 (1995), 423–426. (1995) MR1364481
  13. Endlichpräsentierbare Moduln, Arch. Math. 20 (1969), 262–266. (1969) MR0244322
  14. Representable equivalences between categories of modules and applications, Rend. Sem. Mat. Univ. Padova 82 (1989), 203–231. (1989) MR1049594
  15. Theory of Categories, Academic Press, New York-London, 1965. (1965) Zbl0136.00604MR0202787
  16. On the endomorphism ring of an infinite dimensional vector space, Proc. Conf. Abelian Groups and Modules (Padova 1994), Kluwer, Dordrecht, 1995, pp. 395–417. (1995) MR1378215
  17. Die Vertauschbarkeit des H o m -Funktors mit direkten Summen, Dissertation, Ludwig-Maximilian-Universität, München, 1967. (1967) 
  18. Sur les modules  M tels que H o m ( M , - ) commute avec les sommes directes, C.  R.  Acad. Sci. Paris 268 (1969), 930–932. (1969) MR0241466
  19. Criteria for steadiness, Proc. Conf. Abelian Groups, Module Theory and Topology (Padova 1997), Marcel Dekker, New York, 1998, pp. 359–371. (1998) MR1651181
  20. Every * -module is finitely generated, J. Algebra 164 (1994), 392–398. (1994) MR1297156
  21. Steady rings may contain large sets of orthogonal idempotents, Proc. Conf. Abelian Groups and Modules (Padova 1994), Kluwer, Dordrecht, 1995, pp. 467–473. (1995) Zbl0845.16009MR1378220
  22. Modules over non-perfect rings, Advances in Algebra and Model Theory, Gordon and Breach, Philadelphia, 1996, pp. 471–492. (1996) MR1687740
  23. Grundlagen der Modul- und Ringtheorie, Verlag R. Fischer, München, 1988. (1988) Zbl0657.16001MR0969132
  24. Steady ideals and rings, Rend. Sem. Mat. Univ. Padova 98 (1997), . (1997) MR1492975
  25. Structure of steady rings, Ph.D.  Thesis, Charles University, Prague, 1998. (1998) 

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