Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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WHEN AN $\mathfrak{S}$-CLOSED SUBMODULE IS A DIRECT SUMMAND

  • Wang, Yongduo (Department of Applied Mathematics Lanzhou University of Technology) ;
  • Wu, Dejun (Department of Applied Mathematics Lanzhou University of Technology)
  • Received : 2011.06.02
  • Published : 2014.05.31
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Abstract

It is well known that a direct sum of CLS-modules is not, in general, a CLS-module. It is proved that if $M=M_1{\oplus}M_2$, where $M_1$ and $M_2$ are CLS-modules such that $M_1$ and $M_2$ are relatively ojective (or $M_1$ is $M_2$-ejective), then M is a CLS-module and some known results are generalized.

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References

  1. E. Akalan, G. F. Birkenmeier, and A. Tercan, Goldie extending modules, Comm. Algebra 37 (2009), no. 2, 663-683. https://doi.org/10.1080/00927870802254843
  2. G. F. Birkenmeier and A. Tercan, When some complement of a submodule is a summand, Comm. Algebra 35 (2007), no. 2, 597-611. https://doi.org/10.1080/00927870601074830
  3. K. R. Goodearl, Ring Theory, Marcel-Dekker, New York, 1976.
  4. A. Harmanci and P. F. Smith, Finite direct sums of CS-modules, Houston J. Math. 19 (1993), no. 4, 523-532.
  5. M. A. Kamal and B. J. Muller, Extending modules over commutative domains, Osaka J. Math. 25 (1988), no. 3, 531-538.
  6. S. H. Mohamed and B. J. Muller, Ojective modules, Comm. Algebra 30 (2002), no. 4, 1817-1827. https://doi.org/10.1081/AGB-120013218
  7. P. F. Smith and A. Tercan, Continuous and quasi-continuous modules, Houston J. Math. 18 (1992), no. 3, 339-348.
  8. A. Tercan, On CLS-modules, Rocky Mountain J. Math. 25 (1995), no. 4, 1557-1564. https://doi.org/10.1216/rmjm/1181072161