Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-18T17:26:12.900Z Has data issue: false hasContentIssue false
  • English
  • Français

On ring extensions of FSG rings

Published online by Cambridge University Press:  17 April 2009

Le Van Thuyet
Le Van Thuyet
Affiliation:
Department of MathematicsHue University of Education32 Le Loi St 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.

A ring R is called right FSG if every finitely generated right R-subgenerator is a generator. In this note we consider the question of when a ring extension of a given right FSG ring is right FSG and the converse. As a consequence we obtain some results about right FSG group rings.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 3 , June 1994 , pp. 365 - 371
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Anderson, F.W. and Fuller, K.R., Rings and categories of modules (Springer-Verlag, Berlin, Heidelberg, New York, 1974).CrossRefGoogle Scholar
[2]Beachy, J.A., ‘Generating and cogenerating structures’, Trans. Amer. Math. Soc. 158 (1971), 75–92.CrossRefGoogle Scholar
[3]Clark, J., ‘The centre of an FPF ring need not be FPF’, Bull. Austral. Math. Soc. 37 (1988), 235–236.CrossRefGoogle Scholar
[4]Clark, J., ‘A note on the fixed subring of an FPF ring’, Bull. Austral. Math. Soc. 40 (1989), 109–111.CrossRefGoogle Scholar
[5]Connell, I., ‘On the group ring’, Canad. J. Math. 15 (1963), 650–685.CrossRefGoogle Scholar
[6]Faith, C. and Page, S., FPF ring theory: Faithful modules and generators of Mod-R, London Math. Soc. Lecture Notes Series 88 (Cambridge Univ. Press, Cambridge, 1984).CrossRefGoogle Scholar
[7]Faith, C. and Pillay, P., Classification of commutative FPF rings, Notes de Mathematica 4 (Universidad de Murcia, 1990).Google Scholar
[8]Van Thuyet, Le, ‘On rings whose finitely generated cofaithful modules are generators’, Algebra Ber. München 70 (1993), 1–38.Google Scholar
[9]Renault, G., ‘Sur les anneaux de groups’, C.R. Acad. Sci. Paris Sér A-B 273 (1971), 84–87.Google Scholar
[10]Renault, G., ‘Sur les anneaux de groupes’, in Rings, modules and radicals 6, Proc. Colloq., Keszthely 1971, pp.371–396 (Colloq. Math. Soc. János Bolyai, North–Holland Amsterdam, 1973).Google Scholar
[11]Wisbauer, R., Grundlagen der modul-und ringtheorie (R. Fischer Verlag, München, 1988).Google Scholar