Transactions of the American Mathematical Society

Author(s): George M. Bergman
Journal: Trans. Amer. Math. Soc. 354 (2002), 2079-2114.
MSC (2000): Primary 05B35, 16K40, 16S90; Secondary 16E60, 16N80, 16S50, 16U20, 18A30
Posted: January 8, 2002
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Abstract: If

is an associative ring, one of several known equivalent types of data determining the structure of an arbitrary division ring

generated by a homomorphic image of

is a rule putting on all free

-modules of finite rank matroid structures (closure operators satisfying the exchange axiom) subject to certain functoriality conditions. This note gives a new description of how

may be constructed from this data. (A classical precursor of this is the construction of $\mathbf Q$ as a field with additive group a direct limit of copies of $\mathbf Z$ .)

The division rings of fractions of right and left Ore rings, the universal division ring of a free ideal ring, and the concept of a specialization of division rings are then interpreted in terms of this construction.

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George M. Bergman
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840
Email: gbergman@math.berkeley.edu

DOI: 10.1090/S0002-9947-02-02927-6
PII: S 0002-9947(02)02927-6
Received by editor(s): January 24, 2000
Received by editor(s) in revised form: August 23, 2001
Posted: January 8, 2002
Additional Notes: Part of this work was done in 1977 while the author was supported by the Miller Institute for Basic Research in the Sciences
The author apologizes to workers in the field who were inconvenienced by the 23-year delay between his getting the main result of this paper, and his finding the time to prepare it for publication
Copyright of article: Copyright 2002, American Mathematical Society

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