Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-19T05:04:33.230Z Has data issue: false hasContentIssue false

On weakly SI-modules

Published online by Cambridge University Press:  17 April 2009

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

Abstract

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.

In this note we characterise finitely generated self-projective R-modules M satisfying the property that every non-zero M-singular. R-module contains a non-zero M-injective submodule.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]van Huynh, D. and Wisbauer, R., ‘A structure theorem for SI-modules’, Glasgow Math. J. 34 (1992), 8389.CrossRefGoogle Scholar
[2]Goodearl, K.R., Singular torsion and the splitting properties (Memoirs of the Amer. Math. Soc., No 124, 1972).CrossRefGoogle Scholar
[3]Michler, G.O. and Villamayor, O.E., ‘On rings whose simple modules are injective’, J.Algebra. 25 (1973), 185201.CrossRefGoogle Scholar
[4]van Sanh, N., ‘On SC-modules’, Bull. Austral. Math. Soc. 48 (1993), 251255.CrossRefGoogle Scholar
[5]Rizvi, S.T. and Yousif, M.F., ‘On continuous and singular modules’, in Non-commutative ring theory, Lecture Notes Math. 1448, Proc. Conf. Athens/OH (USA) 1989 (Springer-Verlag, Berlin, Heidelberg, New York, 1990), pp. 116124.CrossRefGoogle Scholar
[6]Wisbauer, R., ‘Generalized co-semisimple modules’, Comm. Algebra 18 (1990), 42354253.CrossRefGoogle Scholar
[7]Wisbauer, R., Foundations of module and ring theory (Gordon and Breach, London, Tokyo, 1991).Google Scholar
[8]Wisbauer, R., ‘Localization of modules and the central closure of rings’, Comm. Algebra 9 (1981), 14551493.CrossRefGoogle Scholar
[9]Yousif, M.F., ‘V-modules with Krull dimension’, Bull. Austral. Math. Soc. 37 (1988), 237240.CrossRefGoogle Scholar