Genera and direct sum decompositions of torsion free modules

D. M. Arnold and E. L. Lady, Endomorphism rings and direct sums of torsion free abelian groups, Trans. A.M.S. 211(1975), 225–237.
Article MathSciNet MATH Google Scholar
R. A. Beaumont and R. S. Pierce, Subrings of algebraic number fields, Acta. Sci. Math. Szeged 22(1961), 202–216.
MathSciNet MATH Google Scholar
_____, Torsion free rings, Ill. Jour. Math. 5(1961), 61–98.
MathSciNet MATH Google Scholar
L. Fuchs, Infinite Abelian Groups, Vol. II, Academic Press, New York, 1973.
MATH Google Scholar
L. Fuchs and F. Loonstra, On direct decompositions of torsion free abelian groups of finite rank, Rend. Sem. Mat. Univ. Padova 44(1970), 75–83.
MathSciNet Google Scholar
K. R. Goodearl, Power cancellation of groups and modules, Pacific J. Math., to appear.
Google Scholar
H. Jacobinski, Genera and decompositions of lattices over orders, Acta. Math. 121(1968), 1–29.
Article MathSciNet MATH Google Scholar
E. L. Lady, Summands of finite rank torsion free abelian groups, J. Alg. 32(1974), 51–52.
Article MathSciNet MATH Google Scholar
_____, Nearly isomorphic torsion free abelian groups, J. Alg. 35(1975), 235–238.
Article MathSciNet MATH Google Scholar
_____, Almost completely decomposable torsion free abelian groups, Proc. A.M.S. 45(1974), 41–47.
Article MathSciNet MATH Google Scholar
R. S. Pierce, Subrings of simple algebras, Michigan Math. J. 7(1960), 241–243.
Article MathSciNet MATH Google Scholar
J. D. Reid, On the ring of quasi-endomorphisms of a torsion free group, Topics in Abelian-Groups, Chicago, 1963, 51–68.
Google Scholar
I. Reiner, Maximal Orders, Academic Press, New York, 1975.
MATH Google Scholar
_____, A survey of integral representation theory, Bull. A.M.S. 76(1970), 159–227.
Article MathSciNet MATH Google Scholar
K. W. Roggenkamp, Lattices over Orders II, Springer-Verlag Lecture notes No. 142, Springer, Berlin, 1970.
MATH Google Scholar
A. V. Roiter, On integral representations belonging to a genus, Izv. Akad. Nauk. USSR 30(1966), 1315–1324.
MathSciNet Google Scholar
R. G. Swan, and E. G. Evans, K-Theory of Finite Groups and Orders, Springer-Verlag Lecture Notes No. 149, Springer, Berlin, 1970.
Google Scholar
R. G. Swan, Projective modules over group rings and maximal orders, Ann. of Math. (2) 76(1962), 55–61.
Article MathSciNet MATH Google Scholar
_____, Algebraic K-Theory, Springer-Verlag Lecture Notes No. 76, Springer, Berlin, 1968.
MATH Google Scholar
R. B. Warfield, Jr., Cancellation for modules and the stable range of endomorphism rings, to appear.
Google Scholar
H. Zassenhaus, Orders as endomorphism rings of modules of the same rank, J. London Math. Soc. 42(1967), 180–182.
Article MathSciNet MATH Google Scholar

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David M. Arnold
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David M. Arnold Roger H. Hunter Elbert A. Walker

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Arnold, D.M. (1977). Genera and direct sum decompositions of torsion free modules. In: Arnold, D.M., Hunter, R.H., Walker, E.A. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068197

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DOI: https://doi.org/10.1007/BFb0068197
Published: 27 August 2006
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08447-1
Online ISBN: 978-3-540-37069-7
eBook Packages: Springer Book Archive

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