Geodesic
$T_1$-separable numberings of subdirectly indecomposable algebras
Algebra i logika, Tome 60 (2021) no. 4, pp. 400-424

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We prove the existence of a natural subclass of subdirectly indecomposable algebras all of whose Hausdorff numberings are negative. We also construct a $T_1$-separable nonnegative subdirectly indecomposable algebra with Artin congruence lattice.
Keywords: subdirect indecomposability, Artinianness, Noetherianness, computable and enumerable topologies, topological numbered algebras, translational precompleteness, positivity, negativity, effective separability. 
@article{AL_2021_60_4_a1,
     author = {N. Kh. Kasymov and A. S. Morozov and I. A. Khodzhamuratova},
     title = {$T_1$-separable numberings of subdirectly indecomposable algebras},
     journal = {Algebra i logika},
     pages = {400--424},
     publisher = {mathdoc},
     volume = {60},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2021_60_4_a1/}
}
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N. Kh. Kasymov; A. S. Morozov; I. A. Khodzhamuratova. $T_1$-separable numberings of subdirectly indecomposable algebras. Algebra i logika, Tome 60 (2021) no. 4, pp. 400-424. http://geodesic.mathdoc.fr/item/AL_2021_60_4_a1/