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Kartashova, Anna Vladimirovna

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

Number of views:
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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, “Ńharacterization of distributive lattices of quasivarieties of unars”, Chebyshevskii Sb., 22:1 (2021),  177–187  mathnet
2014
2. A. V. Kartashova, “On Commutative Unary Algebras with Totally Ordered Congruence Lattice”, Mat. Zametki, 95:1 (2014),  80–92  mathnet  mathscinet  elib; Math. Notes, 95:1 (2014), 67–77  isi  elib  scopus
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  mathnet  elib
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  mathnet
2011
5. A. V. Kartashova, “Antivarieties of unars”, Algebra Logika, 50:4 (2011),  521–532  mathnet  mathscinet  zmath; Algebra and Logic, 50:4 (2011), 357–364  isi  scopus
6. A. V. Kartashova, “On congruence lattices and topology lattices of unary algebras”, Chebyshevskii Sb., 12:2 (2011),  27–33  mathnet  mathscinet
2009
7. A. V. Kartashova, “On finite lattices of topologies of commutative unary algebras”, Diskr. Mat., 21:3 (2009),  119–131  mathnet  mathscinet  elib; Discrete Math. Appl., 19:4 (2009), 431–443  scopus
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  mathnet  mathscinet; 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  mathnet  mathscinet  elib; J. Math. Sci., 163:6 (2009), 682–687  elib  scopus
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  mathnet  mathscinet  zmath; J. Math. Sci., 144:2 (2007), 3949–3954  scopus
2000
11. A. V. Kartashova, “Topology lattices of unary algebras”, Uspekhi Mat. Nauk, 55:6(336) (2000),  141–142  mathnet  mathscinet  zmath; Russian Math. Surveys, 55:6 (2000), 1152–1153  isi  scopus

Presentations in Math-Net.Ru
1. The structure of distributive topology lattices of commutative unary algebras
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 Mikhailovich
May 29, 2018 16:00
2. Direct sums of strongly connected unary algebras, their identities and quasiidentities
V. 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 Mikhailovich
May 29, 2018 15:00

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