| Title:
|
Modules commuting (via Hom) with some colimits (English) |
| Author:
|
Bashir, Robert El |
| Author:
|
Kepka, Tomáš |
| Author:
|
Němec, Petr |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
891-905 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For every module $M$ we have a natural monomorphism \[ \Psi :\coprod _{i\in I}\mathop {\mathrm Hom}\nolimits _R(M,A_i)\rightarrow \mathop {\mathrm Hom}\nolimits _R\biggl (M,\coprod _{i\in I}A_i\biggr ) \] and we focus our attention on the case when $\Psi $ is also an epimorphism. Some other colimits are also considered. (English) |
| Keyword:
|
module |
| Keyword:
|
colimit |
| Keyword:
|
finitely presented module |
| MSC:
|
16B99 |
| MSC:
|
16D10 |
| MSC:
|
16E30 |
| MSC:
|
18A35 |
| idZBL:
|
Zbl 1080.16504 |
| idMR:
|
MR2018837 |
| . |
| Date available:
|
2009-09-24T11:07:30Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127847 |
| . |
| Reference:
|
[1] H. Bass: Algebraic $K$-Theory.W. A. Benjamin, New York, 1968. Zbl 0174.30302, MR 0249491 |
| Reference:
|
[2] R. Colpi and C. Menini: On the structure of $\ast $-modules.J. Algebra 158 (1993), 400–419. MR 1226797 |
| Reference:
|
[3] R. Colpi and J. Trlifaj: Classes of generalized $\ast $-modules.Comm. Algebra 22 (1994), 3985–3995. MR 1280103, 10.1080/00927879408825060 |
| Reference:
|
[4] P. C. Eklof, K. R. Goodearl and J. Trlifaj: Dually slender modules and steady rings.Forum Math. 9 (1997), 61–74. MR 1426454 |
| Reference:
|
[5] P. C. Eklof and A. H. Mekler: Almost Free Modules.North-Holland, New York, 1990. MR 1055083 |
| Reference:
|
[6] R. El Bashir and T. Kepka: Modules commuting (via $\mathop {\mathrm Hom}\nolimits $) with some limits.Fund. Math. 155 (1998), 271–292. MR 1607449 |
| Reference:
|
[7] P. Freyd: Abelian Categories., New York, 1964. Zbl 0121.02103 |
| Reference:
|
[8] L. Fuchs and L. Salce: Modules over Valuation Domains.Marcel Dekker, New York, 1985. MR 0786121 |
| Reference:
|
[9] A. Gollová: $\sum $-compact modules and steady rings.Ph.D. Thesis, Charles University, Prague, 1997. |
| Reference:
|
[10] J. L. Gómez Pardo, G. Militaru and C. Nǎstǎsescu: When is ${\mathrm HOM}_R(M,-)$ equal to ${\mathrm Hom}_R(M,-)$ in the category $R-{\mathrm gr}$? Comm.Algebra 22 (1994), 3171–3181. MR 1272380 |
| Reference:
|
[11] T. Head: Preservation of coproducts by ${\mathrm Hom}_R(M,-)$.Rocky Mountain J. Math. 2 (1972), 235–237. MR 0294388, 10.1216/RMJ-1972-2-2-235 |
| Reference:
|
[12] T. Kepka: $\cap $-compact modules.Comment. Math. Univ. Carolin. 36 (1995), 423–426. MR 1364481 |
| Reference:
|
[13] H. Lenzing: Endlichpräsentierbare Moduln.Arch. Math. 20 (1969), 262–266. MR 0244322 |
| Reference:
|
[14] C. Menini and A. Orsatti: Representable equivalences between categories of modules and applications.Rend. Sem. Mat. Univ. Padova 82 (1989), 203–231. MR 1049594 |
| Reference:
|
[15] B. Mitchell: Theory of Categories.Academic Press, New York-London, 1965. Zbl 0136.00604, MR 0202787 |
| Reference:
|
[16] A. Orsatti and N. Rodinò: On the endomorphism ring of an infinite dimensional vector space.Proc. Conf. Abelian Groups and Modules (Padova 1994), Kluwer, Dordrecht, 1995, pp. 395–417. MR 1378215 |
| Reference:
|
[17] R. Rentschler: Die Vertauschbarkeit des $\mathop {\mathrm Hom}\nolimits $-Funktors mit direkten Summen.Dissertation, Ludwig-Maximilian-Universität, München, 1967. |
| Reference:
|
[18] R. Rentschler: Sur les modules $M$ tels que $\mathop {\mathrm Hom}\nolimits (M,-)$ commute avec les sommes directes.C. R. Acad. Sci. Paris 268 (1969), 930–932. MR 0241466 |
| Reference:
|
[19] P. Růžička, J. Trlifaj and J. Žemlička: Criteria for steadiness.Proc. Conf. Abelian Groups, Module Theory and Topology (Padova 1997), Marcel Dekker, New York, 1998, pp. 359–371. MR 1651181 |
| Reference:
|
[20] J. Trlifaj: Every $\ast $-module is finitely generated.J. Algebra 164 (1994), 392–398. MR 1297156 |
| Reference:
|
[21] J. Trlifaj: Steady rings may contain large sets of orthogonal idempotents.Proc. Conf. Abelian Groups and Modules (Padova 1994), Kluwer, Dordrecht, 1995, pp. 467–473. Zbl 0845.16009, MR 1378220 |
| Reference:
|
[22] J. Trlifaj: Modules over non-perfect rings.Advances in Algebra and Model Theory, Gordon and Breach, Philadelphia, 1996, pp. 471–492. MR 1687740 |
| Reference:
|
[23] R. Wisbauer: Grundlagen der Modul- und Ringtheorie.Verlag R. Fischer, München, 1988. Zbl 0657.16001, MR 0969132 |
| Reference:
|
[24] J. Žemlička and J. Trlifaj: Steady ideals and rings.Rend. Sem. Mat. Univ. Padova 98 (1997), . MR 1492975 |
| Reference:
|
[25] J. Žemlička: Structure of steady rings.Ph.D. Thesis, Charles University, Prague, 1998. |
| . |
