Linear Ultrafilters
نویسندگان
چکیده
Let X be a k-vector space, and U a maximal proper filter of subspaces of X. Then the ring of endomorphisms of X that are ‘‘continuous’’ with respect to U modulo the ideal of those that are ‘‘trivial’’ with respect to U forms a division ring E(U ). (These division rings can also be described as the endomorphism rings of the simple left End( X )-modules.) We study this and the dual construction, based on maximal cofilters of subspaces of X; in particular, the relation between the constructed division rings and the original field or division ring k. We end by examining a more general construction in which X is a module over a general ring, given with both a filter and a cofilter of
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