Constructing Division Rings as Module-theoretic Direct Limits
نویسنده
چکیده
If R is an associative ring, one of several known equivalent types of data determining the structure of an arbitrary division ring D generated by a homomorphic image of R is a rule putting on all free R-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 D may be constructed from this data. (A classical precursor of this is the construction of Q as a field with additive group a direct limit of copies of 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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تاریخ انتشار 2002