Completely decomposable flat modules over locally factorial domains

Lady, E. L.

doi:10.1090/S0002-9939-1976-0387265-6

Completely decomposable flat modules over locally factorial domains
HTML articles powered by AMS MathViewer

by E. L. Lady

Proc. Amer. Math. Soc. 54 (1976), 27-31

DOI: https://doi.org/10.1090/S0002-9939-1976-0387265-6

PDF | Request permission

Abstract:

Rank $1$ flat modules are classified for a locally factorial noetherian domain by extending the concept of divisor. A direct sum of rank one flat modules in called completely decomposable. A summand of a completely decomposable module is a direct sum of homogeneous components but need not be completely decomposable.

References

D. M. Arnold and E. L. Lady, Endomorphism rings and direct sums of torsion free abelian groups, Trans. Amer. Math. Soc. 211 (1975), 225–237. MR 417314, DOI 10.1090/S0002-9947-1975-0417314-1

Commutative algebra

Robert M. Fossum, The divisor class group of a Krull domain, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 74, Springer-Verlag, New York-Heidelberg, 1973. MR 0382254
László Fuchs, Infinite abelian groups. Vol. II, Pure and Applied Mathematics. Vol. 36-II, Academic Press, New York-London, 1973. MR 0349869
Irving Kaplansky, Commutative rings, Revised edition, University of Chicago Press, Chicago, Ill.-London, 1974. MR 0345945
Daniel Lazard, Autour de la platitude, Bull. Soc. Math. France 97 (1969), 81–128 (French). MR 254100

Bibliographic Information

Journal: Proc. Amer. Math. Soc. 54 (1976), 27-31
DOI: https://doi.org/10.1090/S0002-9939-1976-0387265-6
MathSciNet review: 0387265