Bibliography for Finite Rank Torsion Free Abelian Groups
This is not a set of references referred to in the book.
Nor is it a comprehensive bibliography.
But it's an attempt to indicate what I consider as the basic landmarks
of the theory of finite-rank torsion free groups
since about 1965.
The research before that time,
laying the basic foundations of the subject,
is already well documented in Fuchs, volume II.
(Much of the later work is well documented
in Arnold's Springer Lecture Notes.
The main purpose of this list is highlighting.
There are almost no citations from the past ten or fifteen years.
This is simply because of my ignorance --
I no longer make a serious attempt to keep up with the field.
If I were to have a student who wanted to seriously learn
these are the papers I would suggest that s/he read.
They are listed in an order which I think
gives a good introduction to the field.
For the moment, this list is very incomplete.
I hope to augment it by fall, 1996.
- D. M. Arnold, Finite Rank Torsion Free Abelian Groups
and Rings, Springer Lecture Notes 931
- R. A. Beaumont and R. S. Pierce, Torsion free rings,
Illinois J. Math. 5 (1961), 61-98.
- R. A. Beaumont and R. S. Pierce, Subrings of algebraic
number fields, Acta Math. Szegd. 22 (1961), 202-16.
- M.C.R. Butler, A class of torsion free groups of finite rank,
Proc. London Math Soc.(3)15 (1965), 680-98.
- D. M. Arnold, A class of pure subgroups of completely
decomposable abelian groups, Proc. Amer. Math Soc. 41 (1973),
- D. M. Arnold and E. L. Lady,
Endomorphism rings and direct sums of torsion free abelian groups,
Trans. Amer. Math Soc. 211 (1975), 225-37.
- C. E. Murley,
The classification of certain classes of torsion free abelian groups,
Pac. J. Math 40 (1972), 647-65.
- Extension of scalars for torsion free modules over dedekind domains,
Symp. Math. (INDAM) 23 (1979), 287-305.
- E. L. Lady,
A seminar on splitting rings for torsion free modules
over dedekind domains, in Abelian Group Theory
Springer Lecture Notes 1006 (1983), 1-48.
- S. Brenner and M.C.R. Butler,
Endomorphism rings of vector spaces and torsion free
abelian groups, J. London Math. Soc. 40 (1965),
- V. Dlab and C.M. Ringel,
Indecomposable representations of graphs and algebras,
Mem. Amer. Math. Soc.(3) 21 (1970), 243-76.
- D. M. Arnold, A duality for torsion free modules
of finite rank over a discrete valuation ring,
Proc. London Math. Soc. (3) 42 (1972), 204-16.
- R. B. Warfield, Homomorphisms and duality for torsion free groups,
Math. Z. 107 (1968), 189-200.
- E. L. Lady, Warfield Duality and rank-one quasi-summands
of tensor products of finite rank locally free modules
over dedekind domains,
J. Algebra 121 (1989), 129-38.