Carriers of torsion-free groups

R. S. Pierce; C. I. Vinsonhaler

Rendiconti del Seminario Matematico della Università di Padova (1990)

  • Volume: 84, page 263-281
  • ISSN: 0041-8994

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Pierce, R. S., and Vinsonhaler, C. I.. "Carriers of torsion-free groups." Rendiconti del Seminario Matematico della Università di Padova 84 (1990): 263-281. <http://eudml.org/doc/108203>.

@article{Pierce1990,
author = {Pierce, R. S., Vinsonhaler, C. I.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {carrier; torsion-free abelian group; subgroups of algebraic number fields; quasi-endomorphism ring; carriers of groups; carriers of rings; Galois group},
language = {eng},
pages = {263-281},
publisher = {Seminario Matematico of the University of Padua},
title = {Carriers of torsion-free groups},
url = {http://eudml.org/doc/108203},
volume = {84},
year = {1990},
}

TY - JOUR
AU - Pierce, R. S.
AU - Vinsonhaler, C. I.
TI - Carriers of torsion-free groups
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1990
PB - Seminario Matematico of the University of Padua
VL - 84
SP - 263
EP - 281
LA - eng
KW - carrier; torsion-free abelian group; subgroups of algebraic number fields; quasi-endomorphism ring; carriers of groups; carriers of rings; Galois group
UR - http://eudml.org/doc/108203
ER -

References

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  2. [A-M] M.F. Atiyah - I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, 1969. Zbl0175.03601MR242802
  3. [A-P-R-V-W] D.M. Arnold - R.S. Pierce - J.D. Reid - C.I. Vinsonhaler- W.J. Wickless, Torsion free abelian groups of finite rank projective as modules over their endomorphism rings, Jour. Alg., 71 (1981), pp. 1-10. Zbl0464.20039MR627421
  4. [B1] M.C.R. Butler, On locally free torsion-free rings of finite rank, J. Lond. Math. Soc., 43 (1968), pp. 297-300. Zbl0155.07202MR225878
  5. [B2] M.C.R. Butler, A Galois-theoretic description of certain quasi-endomorphism rings, Symposia Mathematica, 13 (1974), pp. 143-151. Zbl0312.16026MR357514
  6. [B-S] R.A. Bowshell - P. Schultz, Unital rings whose additive endomorphisms commute, Math. Ann., 228 (1977), pp. 197-214. Zbl0336.20040MR498691
  7. [C] A.L.S. Corner, Every countable reduced torsion-free ring is an endomorphism ring, Proc. Lond. Math. Soc., (3), 13 (1963), pp. 687-710. Zbl0116.02403MR153743
  8. [D-V-M] M. Dugas - A. Mader - C.I. Vinsonhaler, Large E-rings exist, J. Algebra, 108 (1987), pp. 88-101. Zbl0616.20026MR887193
  9. [J] N. Jacobson, Lectures in Abstract Algebra, vol. III, Von Nostrand, Princeton, 1964. Zbl0124.27002
  10. [K] G. KolettisJr., Homogeneously decomposable modutes, Studies on Abelian Groups, Paris (1968), pp. 223-238. Zbl0213.30802MR244228
  11. [M-V] A. Mader - C.I. Vinsonhaler, Torsion-free E-modules, J. Alg., 115 (1988), pp. 401-411. Zbl0639.13010MR943264
  12. [N] J. Neukirch, Class Field Theory, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1980. Zbl0587.12001MR819231
  13. [P1] R.S. Pierce, Subrings of simple algebras, Mich. Math. J., 7 (1960), pp. 241-243. Zbl0103.26803MR148707
  14. [P2] R.S. Pierce, Permutation representations with trivial set stabilizers, J. Alg., 95 (1985), pp. 88-95. Zbl0595.20007MR797657
  15. [P-V1] R.S. Pierce - C.I. Vinsonhaler, Realizing central division algebras, Pac. J. Math., 109 (1983), pp. 165-177; correction, 130 (1987), pp. 397-399. Zbl0533.16009MR716296
  16. [P-V2] R.S. Pierce - C.I. Vinsonhalfr, Realizing algebraic number fields, Lecture Notes in Mathematics, 1006, Springer-Verlag, New York (1982/83), pp. 49-96. Zbl0515.12006MR722613
  17. [P-V3] R.S. Pierce- C.I. Vinsonhaler, Classifying E-rings (manuscript). Zbl0728.20047
  18. [Re] J.D. Reid, On the ring of quasi-endomorphisms of a torsion-free group Topics in Abelian Groups, Chicago (1963), pp. 51-68. MR169915
  19. [Ri] P. Ribenboim, Modules sur un anneau de Dedekind, Summa Brasil Math., 3 (1952), pp. 21-36. Zbl0049.16001MR55976
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  21. [W] E. Weiss, Algebraic Number Theory, McGraw-Hill, New York, 1963. Zbl0115.03601MR159805
  22. [Z] H. Zassenhaus, Orders as endomorphism rings of modules of the same rank, J. Lond. Math. Soc., 42 (1967), pp. 180-182. Zbl0145.26405MR206051

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