On Left SF-Rings and Strongly Regular Rings
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
A ring R called left SF if its simple left modules are flat. Regular rings are known to be left SF-rings. However, till date it is unknown whether a left SF-ring is necessarily regular. In this paper, we prove the strong regularity of left (right) complement bounded left SF-rings. We also prove the strong regularity of a class of generalized semicommutative left SF-rings.
Abstract
A ring R called left SF if its simple left modules are flat. Regular rings are known to be left SF-rings. However, till date it is unknown whether a left SF-ring is necessarily regular. In this paper, we prove the strong regularity of left (right) complement bounded left SF-rings. We also prove the strong regularity of a class of generalized semicommutative left SF-rings.
참고문헌 (11)
- H. E. Abulkheir, "Right complement bounded semiprime rings", Acta. Math. Hungar, 70(3), pp.227~235 (1996)
- V. S. Ramamurthy, "On the injectivity and atness of certain cyclic modules", Proc. Amer. Math. Soc., 48, pp.21~25 (1975)
- M. B. Rege, "On von Neumann regular rings and SF-rings", Math. Japonica, 31(6), pp.927~936 (1986)
- Y. Xiao, "One sided SF-rings with certain chain conditions", Canad. Math. Bull, 37(2), pp.272~277 (1994)
- R. Yue Chi Ming, "Annihilators and strongly regular rings", Rend. Sem.Fac. Sc. Univ. Cagliari, 57, pp.51~59 (1987)
- R. Yue Chi Ming, "On Von Neumann regular rings XV", Acta Mathematica Vietnamica, 23, pp.71~79 (1988)
- R. Yue., "Chi Ming: On rings close to regular and p-injectivity", Commentationes Math-ematicae Universitatis, 47(2), pp.203~212 (2006)
- J. Zhang, "Left SF-rings whose complement left ideals are ideals", Acta Mathematica Vietnamica, 17(1), pp.157~159 (1992)
- J. Zhang, "Von Neumann regularity of SF-rings", Communications in Algebra, 21(7), pp.2445~2451 (1993)
- J. Zhang, "Strongly regular rings and SF-rings", Northeast. Math. J., 14(1), pp.61~68 (1998)
- H. Zhou, "Left SF-rings and regular rings", Communications in Algebra, 35, pp.3842~3850 (2007)