Linear Topologies On a Ring an Overview

by Golan

Linear topologies on a noncommutative ring R are determined by 'topologizing' filters of left ideals of R. This Research Note presents a unified study of the set of R-fil of all such filters, with emphasis on the interplay between the order of algebraic structures naturally defined on it. Thus, R-fil is considered first as a complete lattice, next as a semiring and thirdly as the dual of a residuated lattice-ordered monoid. A construction due to Levitzki is adapted to show how arbitrarily-large transifnite products may be defined in R-fil. Emphasis is also placed on the idempotent elements of R-fil, which correspond to torsion theories on module categories over R, and the way in which they sit in R-fil.

128 pages, Paperback

First published January 1, 1987