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论Clean环的性质与扩张 被引量：1

On the Properties and Extensions of Clean Rings
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摘要 根据W.K.Nicholson,Y.Zhou给出的一般chean环的定义,对Clean环的几个重要性质进行了论述,并在此基础上讨论了一般clean环的扩张,对Clean环是Morita不变量在一定条件下进行了阐述. This paper has by W. K. Nicholson and well. discussed several important Y.Zhou, and it has also properties of Clean Rings on the basis of the definition given discussed some extension properties and Morita invariant as
作者 唐再良 张清
机构地区 绵阳师范学院数学与信息科学系
出处 《西华师范大学学报（自然科学版）》 2007年第3期246-248,共3页 Journal of China West Normal University(Natural Sciences)
基金 四川省教育厅科研基金资助项目(2006A141)
关键词 CLEAN环 Von Neumann正则环 一般clean环 Morita不变量 Clean Rings Von Neumann regular rings general clean rings Morita invariant
分类号 O153.3 [理学—基础数学]
  • 相关文献

参考文献14

  • 1NICHOLSON W K,ZHOU Y. Clean General Rings[ J]. Journal of Algebra,2005,291:297 -311.
  • 2LIU Z K. Baer Rings of Generalized Power Series[ J ]. Glasgow Math Journal,2002,44:463 - 469.
  • 3HAGHANY A, VARADARAJAN K. Study of Formal Triangular Matrix Rings [ J ]. Communications in Algebra, 1999,27 ( 11 ) : 5507 - 5525.
  • 4YE Y Q. Semiclean Rings[ J]. Comm. Algebra,2003,31:5609 -5625.
  • 5XIAO G S. n-Clean Rings and Weakly Unit Stable Range Rings[J]. Comm. Algebra,2005,33:1501 -1517.
  • 6LIU Z K. Special Properties of Rings of Generalized Power Series [ J ]. Comm. Algebra,2004,3 (8) :3215 -3226.
  • 7AZARPANAH F. When is $ C (X) $ a chean Ring? [ J ]. Acta. Math. Hungar. 2002,94:53 - 58.
  • 8NICHOLSON W K. Strongly Clean Rings and Fitting's Lemma [ J ]. Comm. Algebra, 1999,27 ( 8 ) :3583 - 3592.
  • 9HAN J, NICHOLSON W K. Extension of Clean Rings[ J ]. Comm. Algebra ,2001,29 (6) :2589 - 2595.
  • 10NICHOLSON W K, VARADARAJAN K. Countable Linear Transformations are Clean Proceedings of the American Mathematical Society, 1998,126 ( 1 ) :61 - 64.

二级参考文献14

  • 1Nicholson W K,Zhou Y.Clean General Rings[J].Journal of Algebra,2005,291:297-311.
  • 2Liu Z K.Baer Rings of Generalized Power Series[J].Glasgow Math Journal,2002,44:463-469.
  • 3Han J,Nicholson W K.Extension of Clean Rings[J].Comm.Algebra,2001,29(6):2 589-2 595.
  • 4Ye Y Q.Semiclean Rings[J].Comm.Algebra,2003,31:5 609-5 625.
  • 5Nicholson W K.Strongly Clean Rings And Fitting's Lemma[J].Comm.Algebra,1999,27(8):3 583-3 592.
  • 6Xiao G Sh.n-Clean Rings and Weakly Unit Stable Range Rings[J].Comm.Algebra,2005,33:1 501-1 517.
  • 7Liu Z K.Special Properties of Rings of Generalized Power Series[J].Comm.Algebra,2004,3(8):3 215-3 226.
  • 8Han,J.Nicholson,W.K.Extensions of clean rings[J].Comm.Algebra,2001,29:2589-2595.
  • 9A.haghany,K.Varadarajan.Study of formal triangularmatrix nngs[J].Comm.Algebra,1999,27:5507-5525.
  • 10Liu,Z.K.Special properties of rings of generalized power series[J].Comm.Algebra.2004,32:3215-3226.

共引文献3

同被引文献12

  • 1余柏林,汪明义.Π-凝聚环的推广[J].四川师范大学学报（自然科学版）,2005,28(3):278-281. 被引量：9
  • 2Vasconcelos W V, Simis A. Projective modules over R[X] ,R a valuation ring are free[J]. Notices Am Math Soc,1971,18:805.
  • 3Swan R G. A simple proof of Gabber' s theorem on projective modules over a localized local ring[J]. Proc AMS,1988,103:1025-1030.
  • 4Hartshorne R. Algebraic Geometry [ M ]. New York, Heidelberg, Berlin: Springer-Verlag, 1977.
  • 5Jones M F, Teply M L. Coherent rings of finite weak global dimension[ J ]. Commun Algebra, 1982,10:493-503.
  • 6Matsumura H. Commutative Algebra[ M ]. 2nd ed. California:The Benjamin/Cummings Publishing Company, Inc, 1980.
  • 7Rotman J J. An Introduction to Homological Algebra[ M]. California :The Benjamin Publishing Company, Inc, 1980.
  • 8Vasconcelos W V. On projective modules of finite rank[ J]. Proc AMS, 1969,22:430-433.
  • 9Wang Fang-gui, Tang Gao-hua. Reflexive modules over coherent GCD-domains[ J]. Commun Algebra,2005,33:3283-3292.
  • 10Kim H. Module-theoretic characterizations of t-linkative domains[J]. Commun Algebra,2008,36:1649-1670.

引证文献1

二级引证文献1

西华师范大学学报（自然科学版）
2007年 第3期

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