Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-27T20:52:26.675Z Has data issue: false hasContentIssue false

On SC-modules

Published online by Cambridge University Press:  17 April 2009

Nguyen Van Sank
Affiliation:
Department of Mathematics, Hue Teachers' Training College, 32 Le Loi Street Hue, Vietnam
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let R be a ring. A right R-module M is called an SC-module if every M-singular right R-module is continuous. The purpose of this note is to give some characterisations of SC-modules.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Camillo, V. and Yousif, M.F., ‘CS-modules with acc or dcc on essential submodules’, Comm. Algebra 19 (1991), 655662.Google Scholar
[2]van Huynh, D., Smith, P.F. and Wisbauer, R., ‘A note on GV-modules with Krull dimension’, Glasgow Math. J. 32 (1990), 389390.CrossRefGoogle Scholar
[3]van Huynh, D. and Wisbauer, R., ‘A structure theorem for SI-modules’, Glasgow Math. J. 34 (1992), 8389.Google Scholar
[4]van Huynh, D., Dung, N.V. and Wisbauer, R., ‘Quasi-injective modules with acc or dcc on essential submodules’, Arch. Math. 53 (1989), 252255.Google Scholar
[5]Goodearl, K.R., ‘Singular torsion and the splitting properties’, Mem. Amer. Math. Soc. 124 (1972).Google Scholar
[6]Mohamed, S.H. and Müller, B.J., Continuous and discrete modules, London Math. Soc. Lecture Notes 147 (Cambridge Univ. Press, 1990).CrossRefGoogle Scholar
[7]Müller, B.J. and Rizvi, S.T., ‘On injective and quasi-continuous modules’, J. Pure Appl.Algebra 28 (1983), 197262.CrossRefGoogle Scholar
[8]Osofsky, B.L. and Smith, P.F., ‘Cyclic modules whose quotients have complement direct summands’, J. Algebra 139 (1991), 342354.CrossRefGoogle Scholar
[9]Rizvi, S.T. and Yousif, M.F., ‘On continuous and singular modules’, in Non-commutative ring theory, Lecture Notes in Mathematics 1448, Proc. Conf., Athens/OH(USA) 1989 (Springer-Verlag, Berlin, Heidelberg, New York, 1990), pp. 116124.CrossRefGoogle Scholar
[10]Wisbauer, R., ‘Generalized co-semisimple modules’, Comm. Algebra 18 (1990), 42354253.CrossRefGoogle Scholar
[11]Wisbauer, R., Foundation of module and ring theory (Gordon and Breach, London, Tokyo, 1991).Google Scholar
[12]Wisbauer, R., ‘Localization of modules and the central closure of rings’, Comm. Algebra 9 (1981), 14551493.CrossRefGoogle Scholar