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On modules which force homogeneous maps to be linear
Author(s):
P.
R.
Fuchs
Journal:
Proc. Amer. Math. Soc.
128
(2000),
5-15.
MSC (1991):
Primary 16D10;
Secondary 16D50, 16E50, 16S90
Posted:
September 9, 1999
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Abstract:
Let  be a ring with identity. We characterize in terms of the left ideal structure of  when every homogeneous map between nonsingular  -modules is linear and answer some earlier questions of the author that remained open.
References:
- 1.
- U. Albrecht and J. Hausen, Non-singular modules and
 -homogeneous maps, Proc. Amer. Math. Soc. 123 (1995), 2381-2389. MR 95j:16026 - 2.
- P. Fuchs, C. J. Maxson, and G. Pilz, On rings for which homogeneous maps are linear, Proc. Amer. Math. Soc. 112 (1991), 1-7. MR 91h:16054
- 3.
- K. R. Goodearl, Simple noetherian rings, the Zalesskii-Neroslavskii examples, in ring theory, Lecture Notes in Mathematics (New York-Berlin) (D. Handelman and J. Lawrence, eds.), no. 734, Springer-Verlag, 1978, pp. 118-130. MR 81b:16009
- 4.
- -, Von Neumann regular rings, Monographs and Studies in Mathematics, no. 4, Pitman, London, 1979. MR 80e:16011
- 5.
- L. H. Rowen, Ring theory, Vol. I, Pure and Applied Mathematics, vol. 127, Academic Press, San Diego, 1988. MR 89h:16001
- 6.
- A. E. Zalesskii and O. M. Neroslavskii, There exist simple noetherian rings with zero divisors but without idempotents, Comm. Algebra 5 (1977), 231-244. MR 55:12761
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Additional Information:
P.
R.
Fuchs
Affiliation:
Department of Mathematics, Johannes Kepler University, A-4040 Linz, Austria
Email:
peter.fuchs@jk.uni-linz.ac.at
DOI:
10.1090/S0002-9939-99-04915-1
PII:
S 0002-9939(99)04915-1
Keywords:
Nonsingular module,
injective hull,
regular ring,
maximal ring of quotients
Received by editor(s):
June 25, 1997
Received by editor(s) in revised form:
January 27, 1998
Posted:
September 9, 1999
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1999,
American Mathematical Society
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