On generalized CS-modules

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• 作者：Qingyi Zeng
• 关键词：direct summand ; S ; closed submodule ; GCS ; module ; singular submodule ; 16S99 ; 16D70 ; 16D20
• 刊名：Czechoslovak Mathematical Journal
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：65
• 期：4
• 页码：891-904
• 全文大小：148 KB
• 参考文献：[1] G. F. Birkenmeier, B. J. Müller, S. Tariq Rizvi: Modules in which every fully invariant submodule is essential in a direct summand. Commun. Algebra 30 (2002), 1395–1415.MATH CrossRef
  [2] A. W. Chatters, S. M. Khuri: Endomorphism rings of modules over non-singular CS rings. J. Lond. Math. Soc., II. Ser. 21 (1980), 434–444.MATH MathSciNet CrossRef
  [3] C. Faith: Algebra. Vol. II: Ring Theory. Grundlehren der Mathematischen Wissenschaften 191, Springer, Berlin, 1976. (In German.)MATH CrossRef
  [4] K. R. Goodearl: Ring Theory. Nonsingular Rings and Modules. Pure and Applied Mathematics 33, Marcel Dekker, New York, 1976.MATH
  [5] S. McAdam: Deep decompositions of modules. Commun. Algebra 26 (1998), 3953–3967.MATH MathSciNet CrossRef
  [6] V. D. Nguyen, V. H. Dinh, P. F. Smith, R. Wisbauer: Extending Modules. Pitman Research Notes in Mathematics Series 313, Longman Scientific & Technical, Harlow, 1994.MATH
  [7] R. Wisbauer: Foundations of Module and Ring Theory. Algebra, Logic and Applications 3, Gordon and Breach Science Publishers, Philadelphia, 1991.MATH
  
• 作者单位：Qingyi Zeng (1)
  
  1. Department of Mathematics, Shaoguan University, Daxue Road No. 288, Zhenjiang, Shaoguan, 512005, Guangdong, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Convex and Discrete Geometry
  Ordinary Differential Equations
  Mathematical Modeling and IndustrialMathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9141

文摘

An S-closed submodule of a module M is a submodule N for which M/N is nonsingular. A module M is called a generalized CS-module (or briefly, GCS-module) if any S-closed submodule N of M is a direct summand of M. Any homomorphic image of a GCS-module is also a GCS-module. Any direct sum of a singular (uniform) module and a semi-simple module is a GCS-module. All nonsingular right R-modules are projective if and only if all right R-modules are GCS-modules. Keywords direct summand S-closed submodule GCS-module singular submodule