Resolutions as directed colimits. Electronic preprint arXiv:2312.07197 [math.AC], 37 pp.
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Notes on limits of accessible categories. Electronic preprint arXiv:2310.16773 [math.CT], 35 pp.
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Semialgebras associated with nonunital algebras and k-linear subcategories. Electronic preprint arXiv:2310.05550 [math.CT], 60 pp.
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Tensor-Hom formalism for modules over nonunital rings. Electronic preprint arXiv:2308.16090 [math.RA], 41 pp.
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Comodules and contramodules over coalgebras associated with locally finite categories. Electronic preprint arXiv:2307.13358 [math.CT], 35 pp.
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Flat comodules and contramodules as directed colimits, and cotorsion periodicity. Electronic preprint arXiv:2306.02734 [math.RA], 44 pp.
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Combinatorial and geometric constructions associated with the Kostant cascade, J. Lie Theory, 33, no. 2 (2023), 497--526
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Automorphisms of finite order, periodic contractions, and Poisson-commutative subalgebras of S(g), Math. Zeitschrift, 303, no. 2 (2023), Article 51.
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Homological full-and-faithfulness of comodule inclusion and contramodule forgetful functors. Electronic preprint arXiv:2301.09561 [math.RA], 43 pp.
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Flat quasi-coherent sheaves as directed colimits, and quasi-coherent cotorsion periodicity. Electronic preprint arXiv:2212.09639 [math.AG], 28 pp.
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Fp-projective periodicity. Journ. of Pure and Appl. Algebra 228 #3 (2024), 107497, 24 pp.
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Differential graded Koszul duality: An introductory survey. Bulletin of the London Math. Society 55 (2023), #4, p.1551-1640.
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Semi-infinite algebraic geometry of quasi-coherent sheaves on ind-schemes: Quasi-coherent torsion sheaves, the semiderived category, and the semitensor product. Birkhäuser/Springer Nature, Cham, Switzerland, 2023. xix+216 стр.
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Exact categories of topological vector spaces with linear topology. Electronic preprint arXiv:2012.15431 [math.CT], 71 pp. Accepted by Moscow Math. Journal.
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Flat commutative ring epimorphisms of almost Krull dimension zero. Journ. of Algebra and its Appl. 22 #3 (2023), 2350060, 18 pp.
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An explicit self-dual construction of complete cotorsion pairs in the relative context. Rendiconti Seminario Matematico Univ. Padova 149 (2023), p.191-253.
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Remarks on derived complete modules and complexes. Mathematische Nachrichten 296 (2023), #2, p.811-839.
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Reductive subalgebras of semisimple Lie algebras and Poisson commutativity, J. Symplectic Geom., 20 no. 4 (2022), 911--926
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Coderived and contraderived categories of locally presentable abelian DG-categories. Electronic preprint arXiv:2210.08237 [math.CT], 68 pp.
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Closure properties of \varinjlim \mathcal C. Journ. of Algebra 606 (2022), p.30-103.
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Exact DG-categories and fully faithful triangulated inclusion functors. Electronic preprint arXiv:2110.08237 [math.CT], 151 pp.
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Projective covers of flat contramodules. Internat. Math. Research Notices 2022, #24, p.19527-19564.
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Relative nonhomogeneous Koszul duality. Frontiers in Mathematics, Birkhäuser/Springer Nature, Cham, Switzerland, 2021. xxix+278 pp.
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Topologically semisimple and topologically perfect topological rings. Publicacions Matemàtiques 66 (2022), #2, p.457-540.
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Pseudo-dualizing complexes of bicomodules and pairs of t-structures. Appl. Categor. Struct. 30 (2022), #2, p.379-416.
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Countably generated flat modules are quite flat. Journ. of Commutative Algebra 14 (2022), #1, p.37-54.
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Contramodules over pro-perfect topological rings. Forum Mathematicum 34 (2022), #1, p.1-39.
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Contramodules. Confluentes Math. 13 (2021), #2, p.93-182.
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Poisson-commutative subalgebras of S(g) associated with involutions, Intern. Math. Res. Notices, 2021, no. 23, 18367--18406.
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Periodic automorphisms, compatible Poisson brackets, and Gaudin subalgebras, Transform. Groups, 26, no. 2 (2021), 641--670
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Compatible Poisson brackets associated with 2-splittings and Poisson commutative subalgebras of S(g), J. London Math. Soc., 103, no. 4 (2021), 1577--1595.
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Ilya B. Shapirovsky. Satisfiability problems on sums of Kripke frames. https://arxiv.org/abs/2012.15347

Nilpotent orbits and mixed gradings of semisimple Lie algebras, Indagationes Mathematicae, 32, no. 5 (2021), 1095-1114
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Derived, coderived, and contraderived categories of locally presentable abelian categories. Journ. of Pure and Appl. Algebra 226 #4 (2022), 106883, 39 pp.
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Unbounded derived categories of small and big modules: Is the natural functor fully faithful? Journ. of Pure and Appl. Algebra 225 #11 (2021), 106722, 23 pp.
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Covers and direct limits: a contramodule-based approach. Math. Zeitschrift 299 (2021), #1-2, p.1-52.
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The tilting-cotilting correspondence. Internat. Math. Research Notices 2021, #1, p.189-274.
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S. Kikot, I. Shapirovsky, and E. Zolin. Modal logics with transitive closure: completeness, decidability, filtration. In Advances in Modal Logic, volume 13, pages 369–388, 2020. ISBN 978-1-84890-341-8. https://arxiv.org/pdf/2011.02205.pdf

Casimir elements associated with Levi subalgebras of simple Lie algebras and their applications, Advances in Math., 374 (2020), Article 107390
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Takiff algebras with polynomial rings of symmetric invariants, Transformation Groups, 25, no.2 (2020), 609--624
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Cofibrant generation of pure monomorphisms. Journal of Algebra 560 (2020), p.1297-1310.
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Poisson-commutative subalgebras and complete integrability on non-regular coadjoint orbits and flag varieties, Math. Zeitschrift, 295 (2020), 101-127.
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Glorious pairs of roots and abelian ideals of a Borel subalgebra, J. Algebraic Combinatorics, 52 (2020), 505-525
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