Publications (27)13.69 Total impact

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ABSTRACT: We will develop the model theory of modules over commutative Bezout domains. In particular we characterize commutative Bezout domains B whose lattice of ppformulae has no width and give some applications to the existence of superdecomposable pure injective Bmodules.Journal of Pure and Applied Algebra 04/2015; 219(4):807829. DOI:10.1016/j.jpaa.2014.04.031 · 0.58 Impact Factor 
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ABSTRACT: We classify indecomposable pure injective modules over domestic string algebras, verifying Ringel's conjecture on the structure of such modules. 
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ABSTRACT: We describe the Ziegler spectrum of a Bézout domain B=D+XQ[X] where D is a principal ideal domain and Q is its field of fractions; in particular we compute the CantorBendixson rank of this space. Using this, we prove the decidability of the theory of Bmodules when D is “sufficiently” recursive.Journal of Symbolic Logic 03/2014; 79(1). DOI:10.1017/jsl.2013.4 · 0.47 Impact Factor 
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ABSTRACT: We classify indecomposable pure injective modules over 1domestic string algebras verifying Ringel’s conjecture on their structure.Algebras and Representation Theory 01/2014; 17(2). DOI:10.1007/s1046801394133 · 0.72 Impact Factor 
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ABSTRACT: Let R be an niterated ring of differential polynomials over a commutative noetherian domain which is a ℚalgebra. We will prove that for every proper ideal I of R, the (n + 1)iterated intersection I(n + 1) of powers of I equals zero. A standard application includes the freeness of nonfinitely generated projective modules over such rings. If I is a proper ideal of the universal enveloping algebra of a finitedimensional solvable Lie algebra over a field of characteristic zero, then we will improve the above estimate by showing that I(2) = 0.Journal of Algebra and Its Applications 05/2013; 12(07). DOI:10.1142/S0219498813500205 · 0.37 Impact Factor 
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ABSTRACT: We prove that every pure projective torsion free module over a (commutative) Bass domain with finite normalization contains a finitely generated direct summand.Journal of Pure and Applied Algebra 04/2013; 217(4):757–762. DOI:10.1016/j.jpaa.2012.09.013 · 0.58 Impact Factor 
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ABSTRACT: We classify all (finitely generated or not) projective modules over a class of semilocal ring constructed using nealy simple uniserial domains. They in turn are connected with noncommutative valuations constructed using embeddings of right ordered groups into skew fields.Journal of Algebra and Its Applications 11/2011; 6(5). DOI:10.1142/S0219498807002521 · 0.37 Impact Factor 
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ABSTRACT: We will describe the torsionfree part of the Ziegler spectrum, both the points and the topology, over the integral group ring of the Klein group. For instance we will show that the Cantor–Bendixson rank of this space is equal to 3.Journal of Pure and Applied Algebra 08/2011; 215(8):17911804. DOI:10.1016/j.jpaa.2010.10.012 · 0.58 Impact Factor 
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ABSTRACT: The paper provides a strategy to classify large (i.e. infinitely generated) lattices over representationfinite orders. A combinatorial criterion to decide whether every large lattice decomposes into finitely generated lattices was given by W. Rump [Proc. Lond. Math. Soc. (3) 91, No. 1, 105128 (2005; Zbl 1087.16011)]. Using Příhoda’s theory of fairsized projective modules, the examples given in that paper are refined, and new results are obtained in cases where a full decomposition into finitely generated lattices is not possible. Kaplanski’s theorem states that every projective module over a ring Λ decomposes into countably generated projectives. Assume that every descending chain I 0 ⊃I 1 ⊃I 2 ⊃⋯ of ideals I n with I n I n+1 =I n+1 for all n eventually stabilizes. (For example, this holds for semilocal Noetherian rings Λ, for a classical order Λ over a Dedekind domain, or for the universal enveloping algebra of a finite dimensional solvable Lie algebra over a field of characteristic zero.) Then any countably generated projective Λmodule P has a greatest finitely generated factor module P/IP, where I is an idempotent ideal of Λ, such that the isomorphism class of P is determined by I and the finitely generated projective Λ/Imodule P/IP. Příhoda’s theory is applied to Auslander orders of representationfinite orders, which yields new insights into the structure of large lattices over orders.Journal of the London Mathematical Society 07/2010; 82(1):125143. DOI:10.1112/jlms/jdq031 · 0.88 Impact Factor 
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ABSTRACT: We classify infinitely generated projective modules over generalized Weyl algebras. For instance, we prove that over such algebras every projective module is a direct sum of finitely generated modules.Journal of Algebra 02/2009; 321(4321):13261342. DOI:10.1016/j.jalgebra.2008.11.015 · 0.60 Impact Factor 
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ABSTRACT: We classify group rings of finite groups over a field F according to the modeltheoretic complexity of the category of their modules. For instance, we prove that, if F contains a primitive cubic root of 1, then the Krull–Gabriel dimension of such rings is 0, 2, or undefined.Journal of the London Mathematical Society 04/2008; DOI:10.1112/jlms/jdn015 · 0.88 Impact Factor 
Article: How to construct a ‘concrete’ superdecomposable pureinjective module over a string algebra
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ABSTRACT: We construct an element in a direct product of finite dimensional modules over a string algebra such that the pureinjective envelope of this element is a superdecomposable module.Journal of Pure and Applied Algebra 04/2008; 212(4212):704717. DOI:10.1016/j.jpaa.2007.06.011 · 0.58 Impact Factor 
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ABSTRACT: We investigate the structure of the socalled Gerasimov–Sakhaev counterexample, which is a particular example of a universal localization, and classify (both finitely and infinitely generated) projective modules over it.Journal of Algebra 04/2008; 319(8319):32593279. DOI:10.1016/j.jalgebra.2007.08.009 · 0.60 Impact Factor 
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ABSTRACT: We characterize rings over which every projective module is a direct sum of finitely generated modules, and give various examples of rings with and without this property.Journal of Algebra 09/2007; 315(1315):454481. DOI:10.1016/j.jalgebra.2007.01.043 · 0.60 Impact Factor 
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ABSTRACT: We show that a strong form (the fully faithful version) of the generating hypothesis, introduced by Freyd in algebraic topology, holds in the derived category of a ring R if and only if R is von Neumann regular. This extends results of the second author (J. Pure Appl. Algebra 208(2), 2007). We also characterize rings for which the original form (the faithful version) of the generating hypothesis holds in the derived category of R. These must be close to von Neumann regular in a precise sense, and, given any of a number of finiteness hypotheses, must be von Neumann regular. However, we construct an example of such a ring that is not von Neumann regular and therefore does not satisfy the strong form of the generating hypothesis.Mathematische Zeitschrift 07/2007; 256(4):789800. DOI:10.1007/s002090070103x · 0.68 Impact Factor 
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ABSTRACT: We prove that, if V is an effectively given commutative valuation domain such that its value group is dense and archimedean, then the theory of all Vmodules is decidable.Annals of Pure and Applied Logic 03/2007; 145(3145):258275. DOI:10.1016/j.apal.2006.09.002 · 0.45 Impact Factor 
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ABSTRACT: String algebras were studied initially by Butler and Ringel. There is a range of combinatorial results on the modules over string algebras. For example, indecomposables over a string algebra are classified by string modules and band modules. In the paper under review the author shows that the multiplicity of a simple module as a composition factor in a composition series for a primitive band module over a domestic string algebra is at most two.Colloquium Mathematicum 01/2007; 108(2):285296. DOI:10.4064/cm108210 · 0.42 Impact Factor 
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ABSTRACT: We prove that every nonfinitely generated projective module over the integral group ring of a polycyclicbyfinite group G is free if and only if G is polycyclic.Journal of Algebra 11/2006; 305(2305):845858. DOI:10.1016/j.jalgebra.2005.12.010 · 0.60 Impact Factor 
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ABSTRACT: We classify the indecomposable pure injective modules over a wide class of domestic string algebras and calculate the Krull–Gabriel dimension of these algebras.Algebras and Representation Theory 08/2006; 9(4):337358. DOI:10.1007/s104680069028z · 0.72 Impact Factor 
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ABSTRACT: We prove that every nonfinitely generated projective module over the integral group ring of a polycyclicbyfinite group G is free if and only if G is polycyclic.
Publication Stats
107  Citations  
13.69  Total Impact Points  
Top Journals
Institutions

2013–2015

Belarusian State University
 Department of Mathematics
Myenyesk, Minsk, Belarus


2011

Plekhanov Russian Academy of Economics
Moskva, Moscow, Russia


2006–2011

The University of Manchester
 School of Mathematics
Manchester, England, United Kingdom


2003–2004

The Ohio State University
 Department of Mathematics
Columbus, Ohio, United States
