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 Statistics Math-Net.Ru Total publications: 11 Scientific articles: 11 Presentations: 2

 Number of views: This page: 683 Abstract pages: 2545 Full texts: 963 References: 302
Associate professor
Candidate of physico-mathematical sciences (2001)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
E-mail: ,
Keywords: universal algebra; lattices connected with algebraic systems; unary algebras; topological algebraic systems.

Subject:

In a number of papers we investigate lattices of topologies on algebras and especially lattices of topologies on unars (i.e., on algebras with one unary operation). Some finiteness conditions on these lattices are studied. The sets of all atoms of lattices of topologies on unars are described. Characterizations of those unars whose lattices of topologies are modular, distributive, complemented, pseudocomplemented, Boolean or chains are obtained. We give necessary and sufficient conditions for a modular lattice to be isomorphic to a lattice of topologies of some unar. The sets of all T_0$,$T_1$, and$T_2$-topologies are also considered. Biography Graduated from Faculty of Mathematics of Volgograd Pedagogical State University (VGPU) in 1998. Ph.D. thesis was defended in 2001. A list of my works contains 18 titles. Main publications: • Kartashova A. V. Cardinalities of lattices of topologies of unars and some related topics // Discussiones Mathematicae. General Algebra and Applications, 2001, 21. http://www.mathnet.ru/eng/person9172 List of publications on Google Scholar List of publications on ZentralBlatt https://mathscinet.ams.org/mathscinet/MRAuthorID/681295 Publications in Math-Net.Ru  2021 1. V. K. Kartashov, A. V. Kartashova, “Ñharacterization of distributive lattices of quasivarieties of unars”, Chebyshevskii Sb., 22:1 (2021), 177–187 2014 2. A. V. Kartashova, “On Commutative Unary Algebras with Totally Ordered Congruence Lattice”, Mat. Zametki, 95:1 (2014), 80–92 ; Math. Notes, 95:1 (2014), 67–77 2013 3. A. V. Kartashova, “On congruence lattices of direct sums of strongly connected commutative unary algebras”, Izv. Saratov Univ. Math. Mech. Inform., 13:4(2) (2013), 57–62 4. V. K. Kartashov, A. V. Kartashova, V. N. Ponomarjov, “On conditions for distributivity or modularity of congruence lattices of commutative unary algebras”, Izv. Saratov Univ. Math. Mech. Inform., 13:4(2) (2013), 52–57 2011 5. A. V. Kartashova, “Antivarieties of unars”, Algebra Logika, 50:4 (2011), 521–532 ; Algebra and Logic, 50:4 (2011), 357–364 6. A. V. Kartashova, “On congruence lattices and topology lattices of unary algebras”, Chebyshevskii Sb., 12:2 (2011), 27–33 2009 7. A. V. Kartashova, “On finite lattices of topologies of commutative unary algebras”, Diskr. Mat., 21:3 (2009), 119–131 ; Discrete Math. Appl., 19:4 (2009), 431–443 8. A. V. Kartashova, “Lattices of topologies of unary algebras of the variety$\mathcal A_{1,1}\$”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, 4,  25–32    ; Russian Math. (Iz. VUZ), 53:4 (2009), 20–25 2008 9. A. V. Kartashova, “On quasiorder lattices and topology lattices of algebras”, Fundam. Prikl. Mat., 14:5 (2008),  85–92      ; J. Math. Sci., 163:6 (2009), 682–687 2005 10. A. V. Kartashova, “An analogue of McKenzie's theorem for topology lattices of finite algebras”, Fundam. Prikl. Mat., 11:3 (2005),  109–117      ; J. Math. Sci., 144:2 (2007), 3949–3954 2000 11. A. V. Kartashova, “Topology lattices of unary algebras”, Uspekhi Mat. Nauk, 55:6(336) (2000),  141–142      ; Russian Math. Surveys, 55:6 (2000), 1152–1153

Presentations in Math-Net.Ru
 1 The structure of distributive topology lattices of commutative unary algebrasA. V. Kartashova XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai MikhailovichMay 29, 2018 16:00 2 Direct sums of strongly connected unary algebras, their identities and quasiidentitiesV. K. Kartashov, A. V. Kartashova XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai MikhailovichMay 29, 2018 15:00

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