Countably thick modules
Abdel-Mohsen, Ali ; Saleh, Mohammad
Archivum Mathematicum, Tome 041 (2005), p. 349-358 / Harvested from Czech Digital Mathematics Library

The purpose of this paper is to further the study of countably thick modules via weak injectivity. Among others, for some classes ${\mathcal M}$ of modules in $ \sigma [M]$ we study when direct sums of modules from ${\mathcal M}$ satisfies a property $\mathbb P$ in $\sigma [M]$. In particular, we get characterization of locally countably thick modules, a generalization of locally q.f.d. modules.

Publié le : 2005-01-01
Classification:  16D50,  16D60,  16D70,  16D90
@article{107965,
     author = {Ali Abdel-Mohsen and Mohammad Saleh},
     title = {Countably thick modules},
     journal = {Archivum Mathematicum},
     volume = {041},
     year = {2005},
     pages = {349-358},
     zbl = {1114.16003},
     mrnumber = {2195489},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107965}
}
Abdel-Mohsen, Ali; Saleh, Mohammad. Countably thick modules. Archivum Mathematicum, Tome 041 (2005) pp. 349-358. http://gdmltest.u-ga.fr/item/107965/

Albu T.; Nastasescu C. Relative finiteness in module theory, Marcel Dekker 1984. (1984) | MR 0749933 | Zbl 0556.16001

Al-Huzali A.; Jain S. K.; López-Permouth S. R. Rings whose cyclics have finite Goldie dimension, J. Algebra 153 (1992), 37–40. (1992) | MR 1195405

Berry D. Modules whose cyclic submodules have finite dimension, Canad. Math. Bull. 19 (1976), 1–6. (1976) | MR 0417244 | Zbl 0335.16025

Brodskii G.; Saleh M.; Thuyet L.; Wisbauer R. On weak injectivity of direct sums of modules, Vietnam J. Math. 26 (1998), 121–127. (1998) | MR 1684323

Brodskii G. Denumerable distributivity, linear compactness and the AB5$^{\ast }$ condition in modules, Russian Acad. Sci. Dokl. Math. 53 (1996), 76–77. (1996)

Brodskii G. The Grothendieck condition AB5$^{\ast }$ and generalizations of module distributivity, Russ. Math. 41 (1997), 1–11. (1997) | MR 1480764

Camillo V. P. Modules whose quotients have finite Goldie dimension, Pacific J. Math. 69 (1977), 337–338. (1977) | MR 0442020 | Zbl 0356.13003

Dung N. V.; Huynh D. V.; Smith P. F.; Wisbauer R. Extending modules, Pitman, London, 1994. (1994) | Zbl 0841.16001

Dhompong S.; Sanwong J.; Plubtieng S.; Tansee H. On modules whose singular subgenerated modules are weakly injective, Algebra Colloq. 8 (2001), 227–236. | MR 1838519

Goel V. K.; Jain S. K. $\pi $-injective modules and rings whose cyclic modules are $\pi $-injective, Comm. Algebra 6 (1978), 59–73. (1978) | MR 0491819

Golan J. S.; López-Permouth S. R. QI-filters and tight modules, Comm. Algebra 19 (1991), 2217–2229. (1991) | MR 1123120

Jain S. K.; López-Permouth S. R. Rings whose cyclics are essentially embeddable in projective modules, J. Algebra 128 (1990), 257–269. (1990) | MR 1031920

Jain S. K. López-Permouth S. R.; Risvi T. A characterization of uniserial rings via continuous and discrete modules, J. Austral. Math. Soc., Ser. A 50 (1991), 197–203. (1991) | MR 1094917

Jain S. K.; López-Permouth S. R.; Saleh M. On weakly projective modules, In: Ring Theory, Proceedings, OSU-Denison conference 1992, World Scientific Press, New Jersey, 1993, 200–208. (1992) | MR 1344231

Jain S. K.; López-Permouth S. R.; Oshiro K.; Saleh M. Weakly projective and weakly injective modules, Canad. J. Math. 34 (1994), 972–981. (1994) | MR 1295126

Jain S. K.; López-Permouth S. R.; Singh S. On a class of QI-rings, Glasgow J. Math. 34 (1992), 75–81. (1992) | MR 1145633

Jain S. K.; López-Permouth S. R. A survey on the theory of weakly injective modules, In: Computational Algebra, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 1994, 205–233. (1994) | MR 1245954

Kurshan A. P. Rings whose cyclic modules have finitely generated socle, J. Algebra 14 (1970), 376–386. (1970) | MR 0260780 | Zbl 0199.35503

López-Permouth S. R. Rings characterized by their weakly injective modules, Glasgow Math. J. 34 (1992), 349–353. (1992) | MR 1181777

Malik S.; Vanaja N. Weak relative injective M-subgenerated modules, Advances in Ring Theory, Birkhauser, 1997, 221–239. (1997) | MR 1602677 | Zbl 0934.16002

Mohamed S.; Muller B.; Singh S. Quasi-dual continuous modules, J. Austral. Math. Soc., Ser. A 39 (1985), 287–299. (1985) | MR 0802719

Mohamed S.; Muller B. Continuous and discrete modules, Cambridge University Press 1990. (1990) | MR 1084376

Saleh M. A note on tightness, Glasgow Math. J. $\mathbf{41}$ (1999), 43–44. (1999) | MR 1689655 | Zbl 0923.16003

Saleh M.; Abdel-Mohsen A. On weak injectivity and weak projectivity, In: Proceedings of the Mathematics Conference, World Scientific Press, New Jersey, 2000, 196–207. | MR 1773029 | Zbl 0985.16002

Saleh M.; Abdel-Mohsen A. A note on weak injectivity, Far East Journal of Mathematical Sciences (FJMS) 11 (2003), 199-20-6. | MR 2020502 | Zbl 1063.16004

Saleh M. On q.f.d. modules and q.f.d. rings, Houston J. Math. 30 (2004), 629–636. | MR 2083867 | Zbl 1070.16002

Sanh N. V.; Shum K. P.; Dhompongsa S.; Wongwai S. On quasi-principally injective modules, Algebra Colloq. 6 (1999), 296–276. (1999) | MR 1809646 | Zbl 0949.16003

Sanh N. V.; Dhompongsa S.; Wongwai S. On generalized q.f.d. modules and rings, Algebra and Combinatorics, Springer-Verlag, 1999, 367–272. (1999) | MR 1733193

Wisbauer R. Foundations of module and ring theory, Gordon and Breach, 1991. (1991) | MR 1144522 | Zbl 0746.16001

Zhou Y. Notes on weakly semisimple rings, Bull. Austral. Math. Soc. 52 (1996), 517–525. (1996) | MR 1358705

Zhou Y. Weak injectivity and module classes, Comm. Algebra $\mathbf{25}$ (1997), 2395–2407. (1997) | MR 1459568 | Zbl 0934.16004