Rings over which all modules are semiregular

被引：0
作者：
Tuganbaev A.A. [1 ]
机构：
[1] Russian University of Trade and Economics, Moscow
来源：
Journal of Mathematical Sciences | 2008年 / 154卷 / 2期
基金：
俄罗斯基础研究基金会;
关键词：
Direct Summand; Injective Module; Jacobson Radical; Direct Decomposition; Artinian Ring;
D O I：
10.1007/s10958-008-9163-7
中图分类号：
学科分类号：
摘要：
For a ring A, it is proved that all A-modules are semiregular if and only if A is an Artinian serial ring and J2(A) = 0. © 2008 Springer Science+Business Media, Inc.
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页码：249 / 255
页数：6
相关论文
共 15 条
[1]  
Abyzov A.N., Closure of weakly regular modules with respect to direct sums, Izv. Vyssh. Uchebn. Zaved., Mat., 9, pp. 3-5, (2003)
[2]  
Abyzov A.N., Weakly regular modules over semiperfect rings, Chebyshevskii Sb., 4, pp. 4-9, (2003)
[3]  
Abyzov A.N., Weakly regular modules, Izv. Vyssh. Uchebn. Zaved., Mat., 3, pp. 3-6, (2004)
[4]  
Faith C., Algebra II, Ring Theory, (1976)
[5]  
Khakmi Kh.I., Strongly regular and weakly regular rings and modules, Izv. Vyssh. Uchebn. Zaved., Mat., 5, pp. 60-65, (1994)
[6]  
Hamza H., I <sub>0</sub>-rings and I <sub>0</sub>-modules, Math. J. Okayama Univ., 40, pp. 91-97, (1998)
[7]  
Nicholson W.K., I-rings, Trans. Amer. Math. Soc., 207, pp. 361-373, (1975)
[8]  
Nicholson W.K., Semiregular modules and rings, Can. J. Math., 28, pp. 1105-1120, (1976)
[9]  
Nicholson W.K., Yousif M.F., Quasi-Frobenius Rings, (2003)
[10]  
Osofsky B.L., Rings all of whose finitely generated modules are injective, Pacific J. Math., 14, pp. 645-650, (1964)
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