Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-10T11:29:13.905Z Has data issue: false hasContentIssue false
  • English
  • Français

Modules arising from some relative injectives

Published online by Cambridge University Press:  17 April 2009

Yiqiang Zhou
Yiqiang Zhou
Affiliation:
Department of MathematicsUniversity of British ColumbiaVancouver BCCanada V6T 1Z2
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.

A ring R is a right SI-ring if every singular right R-module is injective, while R is a right S3I-ring if every singular semisimple right R-module is injective. In this paper, we investigate and characterise several analogues of the two notions to modules, with many illustrative examples included.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 2 , April 1996 , pp. 249 - 260
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Anderson, F.W. and Fuller, K.R., Rings and categories of modules (Springer-Verlag, Berlin, Heidelberg, New York, 1994).Google Scholar
[2]Baccella, G., ‘Generalized V-rings and non Neumann regular rings’, Rend. Sem. Mat. Univ. Padova 72 (1984), 117–133.Google Scholar
[3]Goodearl, K.R., ‘Singular torsion and the splitting properties’, Mem. Amer. Math. Soc. 124 (1972).Google Scholar
[4]Harmanci, A. and Smith, P.F., ‘Relative injectivity and module classes’, Comm. Algebra 20 (1992), 2471–2502.Google Scholar
[5]Hirano, Y., ‘Regular modules and V-modules’, Hiroshima Math. J. 11 (1981), 125–142.Google Scholar
[6]Huynh, D.V., Dung, N.V. and Wisbauer, R., ‘On modules with finite uniform and Krull dimension’, Arch. Math. 57 (1991), 122–132.Google Scholar
[7]Huynh, D.V., Smith, P.F. and Wisbauer, R., ‘A note on GV-modules with Krull dimension’, Glasgow Math. J. 32 (1990), 389–390.Google Scholar
[8]Huynh, D.V. and Wisbauer, R., ‘A structure theorem for SI-modules’, Glasgow Math. J. 34 (1992), 83–89.Google Scholar
[9]Mohamed, S.H. and Müller, B.J., Continuous modules and discrete modules (Cambridge University Press, Cambridge, 1990).Google Scholar
[10]Osofsky, B.L., ‘Rings all of whose finitely generated modules are injective’, Pacific J. Math. 14 (1964), 645–650.CrossRefGoogle Scholar
[11]Osofsky, B.L. and Smith, P.F., ‘Cyclic modules whose quotients have complements direct summands’, J. Algebra 139 (1991), 342–354.Google Scholar
[12]Page, S.S. and Yousif, M.F., ‘Relative injectivity and chain conditions’, Comm. Algebra 17 (1989), 899–924.CrossRefGoogle Scholar
[13]Shock, R.C., ‘Dual generalizations of the Artinian and Noetherian conditions’, Pacific J. Math. 54 (1974), 227–235.Google Scholar
[14]Tomonaga, H., ‘On s-unital rings’, Math. J. Okayama Univ. 18 (1976), 117–134.Google Scholar
[15]Wisbauer, R., ‘Localization of modules and central closure of rings’, Comm. Algebra 9 (1981), 1455–1493.Google Scholar
[16]Wisbauer, R., ‘Generalized co-semisimple modules’, Comm. Algebra 8 (1990), 4235–4253.Google Scholar
[17]Wisbauer, R., Foundations of modules and ring theory (Gordon and Breach Science Publishers, 1991).Google Scholar
[18]Yousif, M.F., ‘SI-modules’, Math. J. Okayama Univ. 28 (1986), 133–146.Google Scholar
[19]Zhou, Y., ‘Direct sums of M-injective modules and module classes’, Comm. Algebra 23 (1995), 927–940.Google Scholar
[20]Zhou, Y., ‘Notes on weakly-semisimple rings’, Bull. Austral. Math. Soc. 52 (1995), 517–525.Google Scholar