Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지

CATENARY MODULES II

  • NAMAZI, S. (Dept. of Mathematics, Shiraz University) ;
  • SHARIF, H. (Dept. of Mathematics, Shiraz University)
  • Received : 2000.05.16
  • Published : 2000.07.30
Download PDF
⟨ Previous Next ⟩

Abstract

An A-module M is catenary if for each pair of prime submodules K and L of M with $K{\subset}L$ all saturated chains of prime submodules of M from K to L have a common finite length. We show that when A is a Noetherian domain, then every finitely generated A-module is catenary if and only if A is a Dedekind domain or a field. Moreover, a torsion-free divisible A-module M is catenary if and only if the vector space M over Q(A) (the field of fractions of A) is finite dimensional.

Keywords

References

  1. An Introduction to Commutative Algebra Atiyah, M.F.;MacDonald, I.G.
  2. Comm. in Algebra v.22 A Principal Ideal Theorem analogue for modules over commutative rings George, S.M.;McCasland, R.L.;Smith, P.F.
  3. Comm. Math. Univ. Sancti Pauli v.33 Prime submodules of modules Lu, C.P.
  4. Comm. in Algebra v.23 Spectra of modules Lu, C.P.
  5. Commutative Ring Theory Matsumura, H.
  6. Comm. in Algebra v.20 Prime submodules McCasland, R.L.;Moore, M.E.
  7. Rocky Mountain J. v.23 Prime submodules of Noetheiran modules McCasland, R.L.;Smith, P.F.
  8. Acta Math. Hungar. v.85 no.3 Catenary modules Namazi, S.;Sharif, H.