Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

A NOTE ON LPI DOMAINS

  • Hu, Kui (College of Sciences Southwest University of Science and Technology) ;
  • Wang, Fanggui (College of Mathematics and Software Science Sichuan Normal University) ;
  • Chen, Hanlin (College of Sciences Southwest University of Science and Technology)
  • Received : 2012.02.03
  • Published : 2013.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

A domain is called an LPI domain if every locally principal ideal is invertible. It is proved in this note that if D is a LPI domain, then D[X] is also an LPI domain. This fact gives a positive answer to an open question put forward by D. D. Anderson and M. Zafrullah.

Keywords

References

  1. D. D. Anderson and M. Zafrullah, Integral domains in which nonzero locally principal ideals are invertible, Comm. Algebra 39 (2011), no. 3, 933-941. https://doi.org/10.1080/00927870903529689
  2. S. Glaz and W. V. Vasconcelos, Flat ideals. II, Manuscripta Math. 22 (1977), no. 4, 325-341. https://doi.org/10.1007/BF01168220
  3. S. Glaz and W. V. Vasconcelos, Flat ideals. III, Comm. Algebra 12 (1984), no. 1-2, 199-227. https://doi.org/10.1080/00927878408822998
  4. J. R. Hedstrom and E. G. Houston, Some remarks on star operations, J. Pure Appl. Algebra 18 (1980), no. 1, 37-44. https://doi.org/10.1016/0022-4049(80)90114-0
  5. G. Picozza and F. Tartarone, Flat ideals and stability in integral domains, J Algebra 324 (2010), no. 8, 1790-1802. https://doi.org/10.1016/j.jalgebra.2010.07.021
  6. J. D. Sally and W. V. Vasconcelos, Flat ideals I, Comm. Algebra 3 (1975), 531-543. https://doi.org/10.1080/00927877508822059
  7. M. Zafrullah, Flatness and invertibility of an ideal, Comm. Algebra 18 (1990), no. 7, 2151-2158. https://doi.org/10.1080/00927879008824014

Cited by

  1. Two questions on domains in which locally principal ideals are invertible vol.16, pp.06, 2017, https://doi.org/10.1142/S0219498817501122