Hostname: page-component-77f85d65b8-jkvpf Total loading time: 0 Render date: 2026-04-18T23:15:20.288Z Has data issue: false hasContentIssue false
  • English
  • Français

On Semiregular Rings whose Finitely Generated Modules Embed in Free Modules

Published online by Cambridge University Press:  20 November 2018

Juan Rada  and
Manuel Saorin
Juan Rada
Affiliation:
Departamento de Matemáticas Universidad de Los Andes Mérida, Venezuela e-mail: juanrada@ciens.ula.ve
Manuel Saorin
Affiliation:
Departamento de Matemáticas Universidad de Murcia. Aptdo. 4021 30100 Espinardo, Murcia Spain e-mail: msaorinc@fcu.um.es
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.

We consider rings as in the title and find the precise obstacle for them not to be Quasi-Frobenius, thus shedding new light on an old open question in Ring Theory. We also find several partial affirmative answers for that question.

Keywords

Primary: 16D1016L60Secondary: 16N20

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 2 , 01 June 1997 , pp. 221 - 230
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Anderson, F. W. and Fuller, K. R., Rings and Categories of Modules, 2nd edition, Springer-Verlag, New York/Heidelberg/Berlin, 1992.Google Scholar
2. Björk, J. E., Radical properties of perfect modules, J. Reine Angew. Math. 245 (1972), 78–86.Google Scholar
3. Colby, R. R., Rings which have flat injective modules, J. Algebra 35 (1975), 239–252.Google Scholar
4. Faith, C., Embedding modules in projectives. A report on a problem, Lecture Notes in Math. 951, Springer-Verlag, Berlin and New York, 1982, pp. 21–40.Google Scholar
5. Gómez Pardo, J. L. and Guil Asensio, P. A., Essential embeddings of cyclic modules in projectives, T.A.M.S., to appear.Google Scholar
6. Johns, B., Annihilator conditions in noetherian rings, J.Algebra 49 (1977), 222–224.Google Scholar
7. Menal, P., On the endomorphism ring of a free module, Publ. Mat. Univ. Aut`onoma Barcelona 27 (1983), 141–154.Google Scholar
8. Nicholson, W. K., Semiregular modules and rings, Can. J. Math. 28 (1976), 1105–1120.Google Scholar
9. Osofsky, B. L., A generalization of Quasi-Frobenius rings, J.Algebra 4 (1966), 373–387.Google Scholar
10. Rutter, E. A. Jr., Two characterizations of Quasi-Frobenius rings, Pacific J. Math. 30 (1969), 777–784.Google Scholar
11. Stenstrom, B., Rings on Quotients, Springer-Verlag, Berlin-New York, 1975.Google Scholar
12. Tolskaja, T. S., When are all cyclic modules essentially embedded in free modules? Mat. Issled. 5 (1970), 187–192.Google Scholar
13. Wisbauer, R., Foundations of module and ring theory, Algebra, Logic and Applications, 3, Gordon & Breach, 1991.Google Scholar