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Quasi-e-locally cyclic torsion-free abelian groups
Author(s):
Manfred
Dugas;
C.
J.
Maxson
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3447-3453.
MSC (2000):
Primary 20K30;
Secondary 16Y30
Posted:
June 28, 2005
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Abstract:
For a torsion-free abelian group  , we investigate the problem of determining when  is maximal as a ring in the near-ring of all  -preserving functions on  . We introduce the concept of quasi- -locally cyclic groups and determine several properties of these abelian groups.
References:
-
- 1.
- Arnold, D. M., Finite Rank Torsion-Free Abelian Groups and Rings, LNM 931, Springer-Verlag, New York, 1982. MR 0665251 (84d:20002)
- 2.
- Arnold, D. M., Abelian Groups and Representations of Finite Partially Ordered Sets, CMS Books in Mathematics, Springer-Verlag, New York, 2000. MR 1764257 (2001g:16030)
- 3.
- Fuchs, L., Infinite Abelian Groups, vols. I and II, Academic Press, New York, 1970 and 1973. MR 0255673 (41:333); MR 0349869 (50:2362)
- 4.
- Hausen, J., Abelian groups whose semi-endomorphisms form a ring, Abelian Groups, Marcel Dekker, New York, 1993, pp. 175-180. MR 1217268 (94c:20096)
- 5.
- Hausen J. and Johnson, J., Centralizer near-rings that are rings, J. Austral. Math. Soc. (Series A) 59, (1995), 173-183. MR 1346625 (96g:16061)
- 6.
- Kreuzer, A. and Maxson, C. J., E-locally cyclic abelian groups and maximal near-rings of mappings, Forum Mathematicum, to appear.
- 7.
- Pilz, G. F., Near-Rings, 2nd ed. North-Holland, 1963. MR 0469981 (57:9761)
- 8.
- Zassenhaus, H., Orders as endomorphism rings of modules of the same rank, J. London Math. Soc. 42, (1967), 180-182. MR 0206051 (34:5876)
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Additional Information:
Manfred
Dugas
Affiliation:
Department of Mathematics, Baylor University, Waco, Texas 76798
Email:
Manfred_Dugas@baylor.edu
C.
J.
Maxson
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email:
cjmaxson@math.tamu.edu
DOI:
10.1090/S0002-9939-05-08226-2
PII:
S 0002-9939(05)08226-2
Keywords:
Torsion-free groups,
endomorphism rings,
near-ring of mappings
Received by editor(s):
July 15, 2004
Posted:
June 28, 2005
Additional Notes:
This paper was written in part while the second author was visiting the mathematics department of the University of Stellenbosch, South Africa. The gracious hospitality received during this visit is gratefully acknowledged.
Communicated by:
Lance W. Small
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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