Abstract:
This paper studies the structure of topologically left Artinian rings in which all strictly principal left ideals are closed. By a strictly principal left ideal of some ring $R$ we mean a left ideal of the form $Rx$ for some element $x$ of the ring. It is proved that any topologically Artinian ring in which all strictly principal left ideals are closed can be represented as a factor ring of a topologically direct sum of rings isomorphic to some rings of all matrices of a fixed finite order over some skew field, where the factor ring is taken over the maximal nilpotent ideal.
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