Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE DECOMPOSITION OF EXTENDING LIFTING MODULES

  • Chang, Chae-Hoon (Information Technology Manpower Development Program Kyungpook National University) ;
  • Shin, Jong-Moon (Department of Mathematics Education Dongguk University)
  • Published : 2009.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

In 1984, Oshiro [11] has studied the decomposition of continuous lifting modules. He obtained the following: every continuous lifting module has an indecomposable decomposition. In this paper, we study extending lifting modules. We show that every extending lifting module has an indecomposable decomposition. This result is an expansion of Oshiro's result mentioned above. And we consider some application of this result.

Keywords

References

  1. F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag, New York, 1992
  2. Y. Baba and M. Harada, On almost M-projectives and almost M-injectives, Tsukuba J. Math. 14 (1990), no. 1, 53–69. https://doi.org/10.21099/tkbjm/1496161318
  3. C. Chang, X-lifting modules over right perfect rings, Bull. Korean Math. Soc. 45 (2008), no. 1, 59-66. https://doi.org/10.4134/BKMS.2008.45.1.059
  4. J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer, Lifting Modules, Supplements and projectivity in module theory. Frontiers in Mathematics. Birkhauser Verlag, Basel, 2006
  5. N. Er, Infinite direct sums of lifting modules, Comm. Algebra 34 (2006), no. 5, 1909-1920 https://doi.org/10.1080/00927870500542903
  6. Y. Kuratomi, On direct sums of lifting modules and internal exchange property, Comm. Algebra 33 (2005), no. 6, 1795-1804 https://doi.org/10.1081/AGB-200063365
  7. Y. Kuratomi and C. Chang, Lifting modules over right perfect rings, Comm. Algebra 35 (2007), no. 10, 3103-3109 https://doi.org/10.1080/00927870701405132
  8. S. H. Mohamed and B. J. Muller, Continuous and Discrete Modules, Cambridge University Press, Cambridge, 1990
  9. S. H. Mohamed and B. J. Muller, The exchange property for quasi-continuous modules, Ring theory (Granville, OH, 1992), 242-247, World Sci. Publ., River Edge, NJ, 1993
  10. S. H. Mohamed and B. J. Muller, Ojective modules, Comm. Algebra 30 (2002), no. 4, 1817-1827 https://doi.org/10.1081/AGB-120013218
  11. K. Oshiro, Lifting modules, extending modules and their applications to QF-rings, Hokkaido Math. J. 13 (1984), no. 3, 310-338 https://doi.org/10.14492/hokmj/1381757705
  12. K. Oshiro, Semiperfect modules and quasisemiperfect modules, Osaka J. Math. 20 (1983), no. 2, 337-372
  13. R. B. Warfield, A Krull-Schmidt theorem for infinite sums of modules, Proc. Amer. Math. Soc. 22 (1969), 460-465 https://doi.org/10.2307/2037078