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<p>This paper studies the structure of topologically left Artinian rings in which all strictly principal left ideals are closed. By a&#xa0;strictly principal left ideal of some ring&#xa0;<i>R</i> we mean a&#xa0;left ideal of the form <i>Rx</i> for some element&#xa0;<i>x</i> 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&#xa0;factor ring of a&#xa0;topologically direct sum of rings isomorphic to some rings of all matrices of a&#xa0;fixed finite order over some skew field, where the factor ring is taken over the maximal nilpotent ideal.</p>

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THE STRUCTURE OF TOPOLOGICALLY LEFT ARTINIAN RINGS IN WHICH ALL STRICTLY PRINCIPAL LEFT IDEALS ARE CLOSED

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • V. V. Tenzina

摘要

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.