Year 2007,
Volume: 1 Issue: 1, 46 - 50, 01.06.2007
Abstract
The Faith-Menal conjecture is one of the three main open conjectures
on QF rings. It says that every right noetherian and left FP-injective
ring is QF. In this paper, it is proved that the conjecture is true if every
nonzero complement left ideal of the ring R is not small (or not singular).
Several known results are then obtained as corollaries.
References
- F.W. Anderson and K.R. Fuller, Rings and Categories of Modules, Springer- Verlag, Berlin-Heidelberg-New York, 1992.
- J.L. Chen and W.X. Li, On artiness of right CF rings, Comm. Algebra, 32(11) (2004), 4485-4494.
- C. Faith and P. Menal, A counter example to a conjecture of Johns, Proc. Amer. Math. Soc., 116 (1992), 21-26.
- C. Faith and P. Menal, The structure of Johns rings, Proc. Amer. Math. Soc., (1994), 1071-1081.
- J. L. G´omez Pardo and P. A. Guil Asensio, Torsionless modules and rings with finite essential socle, Lecture Notes in Pure and Appl. Math., 201, New York, Marcel Dekker, 1998, 261-278.
- K.R.Goodearl and R.B. Warfield, An Introduction to Noncommutative Noe- therian Rings, London Mathematical Society Student Texts 16, Cambridge University Press, 1989.
- B. Johns, Annihilator conditions in noetherian rings, J. Algebra, 49 (1977), 224.
- R.P. Kurshan, Rings whose cyclic modules have finitely genrated socle, J. Al- gebra, 15 (1970), 376-386.
- T. Y. Lam, Lectures on Modules and Rings, Springer/Verlag, New York, 1998.
- W.K. Nicholson and M.F.Yousif, Annihilators and the CS-condition, Glasgow Math. J., 40 (1998), 548-578.
- W.K. Nicholson and M.F. Yousif, Quasi-Frobenius Rings, Cambridge Univer- sity Press, Cambridge, 2003.
- E. A. Rutter, Rings with the principal extension property, Comm. Algebra, (3) (1975), 203-212.
- L. Shen and J.L. Chen, New characterizations of quasi-Frobenius rings, Comm. Algebra, 34 (2006), 2157-2165. Liang Shen
- Department of Mathematics, Southeast University Nanjing 210096, P.R. China e-mail: lshen@seu.edu.cn
Year 2007,
Volume: 1 Issue: 1, 46 - 50, 01.06.2007
Abstract
References
- F.W. Anderson and K.R. Fuller, Rings and Categories of Modules, Springer- Verlag, Berlin-Heidelberg-New York, 1992.
- J.L. Chen and W.X. Li, On artiness of right CF rings, Comm. Algebra, 32(11) (2004), 4485-4494.
- C. Faith and P. Menal, A counter example to a conjecture of Johns, Proc. Amer. Math. Soc., 116 (1992), 21-26.
- C. Faith and P. Menal, The structure of Johns rings, Proc. Amer. Math. Soc., (1994), 1071-1081.
- J. L. G´omez Pardo and P. A. Guil Asensio, Torsionless modules and rings with finite essential socle, Lecture Notes in Pure and Appl. Math., 201, New York, Marcel Dekker, 1998, 261-278.
- K.R.Goodearl and R.B. Warfield, An Introduction to Noncommutative Noe- therian Rings, London Mathematical Society Student Texts 16, Cambridge University Press, 1989.
- B. Johns, Annihilator conditions in noetherian rings, J. Algebra, 49 (1977), 224.
- R.P. Kurshan, Rings whose cyclic modules have finitely genrated socle, J. Al- gebra, 15 (1970), 376-386.
- T. Y. Lam, Lectures on Modules and Rings, Springer/Verlag, New York, 1998.
- W.K. Nicholson and M.F.Yousif, Annihilators and the CS-condition, Glasgow Math. J., 40 (1998), 548-578.
- W.K. Nicholson and M.F. Yousif, Quasi-Frobenius Rings, Cambridge Univer- sity Press, Cambridge, 2003.
- E. A. Rutter, Rings with the principal extension property, Comm. Algebra, (3) (1975), 203-212.
- L. Shen and J.L. Chen, New characterizations of quasi-Frobenius rings, Comm. Algebra, 34 (2006), 2157-2165. Liang Shen
- Department of Mathematics, Southeast University Nanjing 210096, P.R. China e-mail: lshen@seu.edu.cn
There are 14 citations in total.
Details
| Other ID | JA95CC96KA |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | June 1, 2007 |
| Published in Issue | Year 2007 Volume: 1 Issue: 1 |