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On semilocal rings

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Abstract

We give several characterizations of semilocal rings and deduce that rationally closed subrings of semisimple artinian rings are semilocal, that artinian modules have semilocal endomorphism rings, and that artinian modules cancel from direct sums.

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References

  1. E.P. Armendariz,Modules with Artinian prime factors, Proc. Amer. Math. Soc.78 (1980), 311–314.

    Article  MATH  MathSciNet  Google Scholar 

  2. E.P. Armendariz, J.W. Fisher and R.L. Snider,On injective endomorphisms of finitely generated modules, Comm. in Algebra6 (1978), 659–672.

    Article  MATH  MathSciNet  Google Scholar 

  3. E.P. Armendariz and J.K. Park,Endomorphism rings of Artinian modules, preprint.

  4. R. Camps and P. Menal,Power cancellation for Artinian modules, Comm. in Algebra19 (1991), 2081–2095.

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Facchini,Loewy and Artinian modules over commutative rings, Annali di Matematica pura ed applicata128 (1980), 359–374.

    Article  MathSciNet  Google Scholar 

  6. J.W. Fisher,Nil subrings of endomorphism rings of modules, Proc. Amer. Math. Soc.34 (1972), 75–78.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Guérindon,Modules de Loewy et modules artiniens, Journal of Algebra79 (1982), 1–7.

    Article  MATH  Google Scholar 

  8. T.Y. Lam,A First Course in Noncommutative Rings, GTM131, Springer-Verlag, Berlin, 1991.

    MATH  Google Scholar 

  9. P. Menal,On π-regular rings whose primitive factor rings are artinian, J. Pure Appl. Algebra20 (1981), 71–78.

    Article  MATH  MathSciNet  Google Scholar 

  10. P. Menal,Cancellation modules over regular rings, inProc. Granada Ring Theory Conference, Lecture Notes in Math.1328, Springer, Berlin, 1988, pp. 187–209.

    Chapter  Google Scholar 

  11. R. Schulz,The endomorphism ring of an artinian module whose homogeneous length is finite, Proc. Amer. Math. Soc.86 (1982), 209–210.

    Article  MATH  MathSciNet  Google Scholar 

  12. J.B. Srivastava and S.K. Shah,Semilocal and semiregular group rings, Indag. Math.42 (1980), 347–352.

    MathSciNet  Google Scholar 

  13. J.T. Stafford,Noetherian full quotient rings, Proc. London Math. Soc.44 (1982), 385–404.

    Article  MATH  MathSciNet  Google Scholar 

  14. R.B. Warfield,A Krull-Schmidt Theorem for infinite sums of modules, Proc. Amer. Math. Soc.22 (1969), 460–465.

    Article  MATH  MathSciNet  Google Scholar 

  15. R.B. Warfield,Cancellation of modules and groups and stable range of endomorphism rings, Pac. J. Math.91 (1980), 457–485.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra (Barcelona), Spain

    Rosa Camps & Warren Dicks

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  1. Rosa Camps
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  2. Warren Dicks
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Dedicated to the memory of Pere Menal

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Camps, R., Dicks, W. On semilocal rings. Israel J. Math. 81, 203–211 (1993). https://doi.org/10.1007/BF02761306

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  • DOI: https://doi.org/10.1007/BF02761306

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