Geodesic
Artinian and Noetherian polygons over completely $0$-simple semigroups
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2024), pp. 67-71

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Necessary and sufficient conditions for act over a completely $0$-simple semigroup to be Artinian and Noetherian are obtained. It is demonstrated that the direct product of Artinian and Noetherian acts, generally speaking, is not Artinian and Noetherian. 
@article{VMUMM_2024_5_a7,
     author = {K. A. Kolesnikova},
     title = {Artinian and {Noetherian} polygons over completely $0$-simple semigroups},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {67--71},
     publisher = {mathdoc},
     number = {5},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2024_5_a7/}
}
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K. A. Kolesnikova. Artinian and Noetherian polygons over completely $0$-simple semigroups. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2024), pp. 67-71. http://geodesic.mathdoc.fr/item/VMUMM_2024_5_a7/