LCM-splitting sets in some ring extensions

@inproceedings{Dumitrescu2002LCMsplittingSI,
  title={LCM-splitting sets in some ring extensions},
  author={T. Dumitrescu and Muhammad Zafrullah},
  year={2002}
}
Let S be a saturated multiplicative set of an integral domain D. Call S an lcm splitting set if dDS ∩ D and dD ∩ sD are principal ideals for every d ∈ D and s ∈ S. We show that if R is an R2-stable overring of D (that is, if whenever a, b ∈ D and aD ∩ bD is principal, it follows that (aD∩bD)R = aR∩bR) and if S is an lcm splitting set of D, then the saturation of S in R is an lcm splitting set in R. Consequently, if D is Noetherian and p ∈ D is a (nonzero) prime element, then p is also a prime… CONTINUE READING

References

Publications referenced by this paper.
SHOWING 1-10 OF 15 REFERENCES

Splitting sets in integral domains

  • M. Zafrullah
  • Proc . Amer . Math Soc .
  • 2001

Zafrullah, Splitting sets in integral domains

  • M.D.D. Anderson
  • Proc. Amer. Math Soc
  • 2001

Cohn’s completely primal elements

  • D. D. Anderson, P.M.M. Zafrullah
  • Lecture Notes in Pure and Applied Mathematics,
  • 1995

Factorization in integral domains II

  • D. F. Anderson, M. Zafrullah
  • J . Algebra
  • 1992

A general theory of almost factoriality

  • M. Zafrullah
  • Manuscripta Math. 51(),
  • 1985

LCM-stableness in ring extensions

  • H. Uda
  • Hiroshima Math. J. 13(),
  • 1983

Zafrullah, The construction D + XDS [X

  • CMZ D. Costa, M. J. Mott
  • J. Algebra
  • 1978

Similar Papers

Loading similar papers…