Geodesic
The structure of topologically left Artinian rings in which all strictly principal left ideals are closed
Fundamentalʹnaâ i prikladnaâ matematika, Tome 25 (2024) no. 1, pp. 213-217

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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. 
@article{FPM_2024_25_1_a11,
     author = {V. V. Tenzina},
     title = {The structure of topologically left {Artinian} rings in which all strictly principal left ideals are closed},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {213--217},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2024_25_1_a11/}
}
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V. V. Tenzina. The structure of topologically left Artinian rings in which all strictly principal left ideals are closed. Fundamentalʹnaâ i prikladnaâ matematika, Tome 25 (2024) no. 1, pp. 213-217. http://geodesic.mathdoc.fr/item/FPM_2024_25_1_a11/