Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-27T16:20:42.141Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalizations of decomposition theorems known over perfect rings

Published online by Cambridge University Press:  09 April 2009

Saad Mohamed  and
Surjeet Singh
Saad Mohamed
Affiliation:
Department of Mathematics, Kuwait University, Kuwait.
Surjeet Singh
Affiliation:
Department of Mathematics, Guru Nanak Dev University, Amritsar, India.
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 paper we introduce and study the notion of dual continuous (d–continuous) modules. A decomposition theorem for a d–continuous module is proved; this generalizes all known decomposition theorems for quasi-projective modules. Besides we study the structure of d–continuous modules over some special types of rings.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 4 , December 1977 , pp. 496 - 510
Copyright
Copyright © Australian Mathematical Society 1977

References

Bass, H. (1960), ‘Finitistic dimension and homological generalization of semi-primary rings’, Trans. Amer. Math. Soc. 95, 466–488.CrossRefGoogle Scholar
Fuchs, L. (1960), Abelian Groups, (Pergamon Press, New York).Google Scholar
Fuchs, L. and Rangaswamy, K. M. (1970), ‘Quasi-projective ahelian groups’, Bull. Soc. Math. France 98, 5–8.CrossRefGoogle Scholar
Koehler, A. (1971), ‘Ouasi-projective and quasi-injective modules’, Pacific J. Math. 36, 713–720.CrossRefGoogle Scholar
Miyashita, Y. (1966), ‘Quasi-projective modules, Perfect modules, and a theorem for modular lattices’, J. Fac. Sci. Hokkaido Univ. 19, 88–110.Google Scholar
Mohamed, S. and Bouhy, T. (1977), ‘Continuous modules’, Arabian J. Sci. and Eng. Dhahran, Saudi Arabia 2, 107–112.Google Scholar
Rangaswamy, K. M. and Vanaja, N. (1972), ‘Quasi-projectives in abelian categories’, Pacific J. Math. 43, 221–238.CrossRefGoogle Scholar
Utumi, Y. (1965), ‘On Continuous rings and self-injective rings’. Trans. Amer. Math. Soc. 118, 158–173.Google Scholar
Wu, L. E. T. and Jans, J. P. (1967), ‘On Quasi-projectives’, Illinois J. Math. 11, 439–448.Google Scholar