01.01.06 (Mathematical logic, algebra, and number theory)
E-mail:
Keywords:
negativity, positivity, separability, enumerations of algebras with finiteness conditions, effectively generated topological spaces, logical specifications of abstract data structures
UDC:
510.6, 510.67, 512, 512.57, 519.68
Subject:
Effectively separable structures and abstract data types
Main publications:
1. Algebras with finitely approximable positively representable enrichments, Kasymov N.Kh., Algebra and Logic, 26, No. 6, 441–450 (1987);
2. Positive algebras with congruences of finite index, Kasymov N.Kh., Algebra and Logic, 30:3, 190–199 (1991);
3. Positive algebras with countable lattices of congruences, Kasymov N.Kh., Algebra and Logic, 31:1, 12–23 (1992);
4. Positive algebras with noetherian congruence lattices, Kasymov N.Kh., Sib.Math.J., 33:2, 338–341 (1992);
5. The number congruences of algebras over simple sets, Kasymov N.Kh., Math.Notes, 52:2, 861-862 (1992);
6. Homomorphisms onto negative algebras, Kasymov N.Kh., Algebra and Logic, 31:2, 81–89 (1992);
7. The number of Q-congruences in positive algebras, Kasymov N.Kh., Algebra and Logic, 31:3, 182–187 (1992);
8. Positive equivalences with finite classes and algebras over them, Kasymov N.Kh., B.M.Khoussainov, Sib.Math.J., 33:5, 923–927 (1992);
9. Nonconstructive negative algebras with finiteness conditions, Kasymov N.Kh., Sib.Math.J., 33:6, 1126–1128 (1992);
10. Separation axioms and partitions of the set of natural numbers, Kasymov N.Kh., Sib.Math.J., 34:3, 468–471 (1993);
11. Enumerated algebras with uniformly recursive-separable classes, Kasymov N.Kh., Sib.Math.J., 34:5, 869–882 (1993);
12. Algebras over negative equivalences, Kasymov N.Kh., Algebra and Logic, 33:1, 46–48 (1994);
13. Recursively separable enumerated algebras, Kasymov N.Kh., Russ.Math.Surv., 51:3, 509-538 (1996) ;
14. Homomorphisms onto effectively separable algebras, Kasymov N.Kh., Sib.Math.J., 57:1, 36–50 (2016);
15. Definability of Linear Orders over Negative Equivalences, N.Kh.Kasymov, A.S.Morozov, Algebra and Logic, 55:1, 24-37 (2016)
N. Kh. Kasymov, “Logical specifications of effectively separable data models”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 6, 15–26
2023
2.
N. Kh. Kasymov, A. S. Morozov, “Lower semilattices of separable congruences of numbered algebras”, Sibirsk. Mat. Zh., 64:4 (2023), 753–769
2022
3.
N. Kh. Kasymov, R. N. Dadazhanov, S. K. Zhavliev, “Uniform $m$-equivalences and numberings of classical systems”, Sib. Èlektron. Mat. Izv., 19:1 (2022), 49–65
4.
R. N. Dadajanov, N. Kh. Kasymov, I. A. Khodzhamuratova, “Uniformly computably separable algebras with effectively splittable families of negative congruences”, Sibirsk. Mat. Zh., 63:3 (2022), 562–575; Siberian Math. J., 63:3 (2022), 466–475
N. Kh. Kasymov, A. S. Morozov, I. A. Khodzhamuratova, “$T_1$-separable numberings of subdirectly indecomposable algebras”, Algebra Logika, 60:4 (2021), 400–424; Algebra and Logic, 60:4 (2021), 263–278
N. Kh. Kasymov, R. N. Dadazhanov, F. N. Ibragimov, “Separable algorithmic representations of classical systems and their applications”, CMFD, 67:4 (2021), 707–754
N. Kh. Kasymov, R. N. Dadazhanov, S. K. Djavliev, “Structures of degrees of negative representations of linear orders”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 12, 31–55; Russian Math. (Iz. VUZ), 65:12 (2021), 27–46
N. Kh. Kasymov, F. N. Ibragimov, “Separable enumerations of division rings and effective embeddability of rings therein”, Sibirsk. Mat. Zh., 60:1 (2019), 82–94; Siberian Math. J., 60:1 (2019), 62–70
N. Kh. Kasymov, I. A. Khodzhamuratova, “Topological Spaces over Algorithmic Representations of Universal Algebras”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 144 (2018), 17–29; Journal of Mathematical Sciences, 245:3 (2020), 311–322
N. Kh. Kasymov, A. S. Morozov, “Definability of linear orders over negative equivalences”, Algebra Logika, 55:1 (2016), 37–57; Algebra and Logic, 55:1 (2016), 24–37
N. Kh. Kasymov, “Separation axioms and partitions of the set of natural numbers”, Sibirsk. Mat. Zh., 34:3 (1993), 81–85; Siberian Math. J., 34:3 (1993), 468–471
N. Kh. Kasymov, B. M. Khusainov, “Positive equivalences with finite classes and algebras over them”, Sibirsk. Mat. Zh., 33:5 (1992), 196–200; Siberian Math. J., 33:5 (1992), 923–927
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