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Product-trace-rings and a question of G. S. Garfinkel
Author(s):
Ralf
Kemper
Journal:
Proc. Amer. Math. Soc.
128
(2000),
709-712.
MSC (1991):
Primary 12J25, 13A18, 13C13, 13E05, 13F30, 13J10, 46N05
Posted:
July 28, 1999
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Abstract:
It is an open question as to whether every left coherent ring  satisfying the intersection property for finitely generated left ideals of  is a right-product-trace-ring or not.  is a right-product-trace-ring iff every product of trace-right- -modules (= universally torsionless-right- -modules) is a trace-right- -module. This question is shown to have a negative answer. Furthermore, looking at all valuation domains, the complete product-trace-rings, the product-trace-rings and the product-content-rings are characterized.
References:
- [1]
- R.L. Ellis: The state of a bounded linear operator on a non-Archimedean normed space; J. Reine Angew. Math., 229 (1968), 155-162. MR 36:6958
- [2]
- O. Endler: Valuation Theory; Springer-Verlag, Berlin, Heidelberg, New York (1972). MR 50:9847
- [3]
- L. Fuchs, L. Salce: Modules over Valuation Domains; Lecture notes in pure and applied mathematics, 97, Marcel Dekker, New York (1985). MR 86h:13008
- [4]
- G. S. Garfinkel: Universally Torsionless and Trace Modules; Trans. Amer. Math. Soc., 215 (1976), 119-144. MR 53:8136
- [5]
- R. Gilmer: Multiplicative Ideal Theory; Pure and Applied Mathematics, 12, Marcel Dekker, New York (1972). MR 55:323
- [6]
- L. Gruson, M. Raynaud: Critères de platitude et de projectivité. Techniques de ``platification'' d'un module; Invent. Math., 13 (1971), 1-89. MR 46:7219
- [7]
- L. Narici, E. Beckenstein, G. Bachmann: Functional Analysis and Valuation Theory; Pure and Applied Mathematics, 5, Marcel Dekker, New York (1971). MR 50:14142
- [8]
- J. Ohm, D.E. Rush: Content Modules and Algebras; Math. Scand., 31 (1972), 49-68. MR 49:9028
- [9]
- A.C.M. van Rooij: Non-Archimedean Functional Analysis; Pure and Applied Mathematics, 51, Marcel Dekker, New York (1978). MR 81a:46084
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Additional Information:
Ralf
Kemper
Affiliation:
Fernuniversität, Fachbereich Mathematik, D 58084 Hagen, Germany
DOI:
10.1090/S0002-9939-99-05098-4
PII:
S 0002-9939(99)05098-4
Keywords:
Trace-module,
universally torsionless module,
product-trace-ring,
((maximally) complete) valuation domain,
spherically complete field,
content-module,
content-ideal
Received by editor(s):
November 25, 1997
Received by editor(s) in revised form:
May 1, 1998
Posted:
July 28, 1999
Dedicated:
Dedicated to H. Röhrl on the occasion of his 70th birthday
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1999,
American Mathematical Society
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