Geodesic
$T_1$-separable numberings of subdirectly indecomposable algebras
Algebra i logika, Tome 60 (2021) no. 4, pp. 400-424
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2021},
     volume = {60},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2021_60_4_a1/}
}
TY  - JOUR
AU  - N. Kh. Kasymov
AU  - A. S. Morozov
AU  - I. A. Khodzhamuratova
TI  - $T_1$-separable numberings of subdirectly indecomposable algebras
JO  - Algebra i logika
PY  - 2021
SP  - 400
EP  - 424
VL  - 60
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/AL_2021_60_4_a1/
LA  - ru
ID  - AL_2021_60_4_a1
ER  - 
%0 Journal Article
%A N. Kh. Kasymov
%A A. S. Morozov
%A I. A. Khodzhamuratova
%T $T_1$-separable numberings of subdirectly indecomposable algebras
%J Algebra i logika
%D 2021
%P 400-424
%V 60
%N 4
%U http://geodesic.mathdoc.fr/item/AL_2021_60_4_a1/
%G ru
%F AL_2021_60_4_a1
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/

[1] G. Birkgof, Teoriya reshetok, Nauka, M., 1984

[2] R. I. Soare, Recursively enumerable sets and degrees. A study of computable functions and computably generated sets, Perspect. Math. Log., Omega Series, Springer-Verlag, Berlin etc., 1987 ; R. I. Soar, Vychislimo perechislimye mnozhestva i stepeni. Izuchenie vychislimykh funktsii i vychislimo perechislimykh mnozhestv, Kazanskoe matem. ob-vo, Kazan, 2000 | DOI

[3] Yu. L. Ershov, Teoriya numeratsii, Nauka, M., 1977

[4] S. S. Goncharov, Yu. L. Ershov, Konstruktivnye modeli, Sibirskaya shkola algebry i logiki, Nauchnaya kniga, Novosibirsk, 1999

[5] A. I. Maltsev, “K obschei teorii algebraicheskikh sistem”, Matem. sb., 35:1 (1954), 3–20 | Zbl

[6] A. I. Maltsev, “Konstruktivnye algebry. 1”, UMN, 16:3 (1961), 3–60 | Zbl

[7] N. Kh. Kasymov, “Rekursivno otdelimye numerovannye algebry”, UMN, 51:3(309) (1996), 145–176 | Zbl

[8] N. Kh. Kasymov, “O gomomorfizmakh na effektivno otdelimye algebry”, Sib. matem. zh., 57:1 (2016), 47–66 | Zbl

[9] N. Kh. Kasymov, I. A. Khodzhamuratova, “Topologicheskie prostranstva nad algoritmicheskimi predstavleniyami universalnykh algebr”, Materialy nauch. konf. “Problemy sovremennoi topologii i ee prilozheniya” (11–12 Maya 2017 g., Tashkent, Uzbekistan), Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 144, VINITI RAN, M., 2018, 17–29

[10] N. Kh. Kasymov, F. N. Ibragimov, “Vychislimo otdelimye modeli”, Sovremennye problemy matematiki i fiziki, 64, no. 4, 2018, 682–705

[11] B. Khoussainov, T. Slaman, P. Semukhin, “$\Pi_1^0$-Presentations of algebras”, Archive Math. Logic, 45:6 (2006), 769–781 | DOI | Zbl

[12] N. Kh. Kasymov, F. N. Ibragimov, “Otdelimye numeratsii tel i effektivnaya vlozhimost v nikh kolets”, Sib. matem. zh., 60:1 (2019), 82–94 | Zbl