Investigation into the structure if algebras  Page description

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Details of project

  
Identifier
43034
Type K
Principal investigator Márki, László
Title in Hungarian Strukturális vizsgálatok algebrákban
Title in English Investigation into the structure if algebras
Panel Natural Sciences Committee Chairs
Department or equivalent Alfréd Rényi Institute of Mathematics
Participants Ágoston, István
Bódi, Béla
Bódi, Viktor
Fialowski, Alice
Fried, Ervin
Kiss, Emil
Lakatos, Piroska
Lukács, Erzsébet
Nagy, Attila
Pham Ngoc, Ánh
Rózsa, Pál
Szigeti, Jenő
Wiegandt, Richárd
Starting date 2003-01-01
Closing date 2007-06-30
Funding (in million HUF) 23.767
FTE (full time equivalent) 0.43
state closed project





 

Final report

  
Results in Hungarian
A következő témákban értünk el eredményeket: - algebrák reprezentációelmélete (kváziöröklődő algebrák, standardul rétegezett algebrák, Coxeter-transzformáció, reciprok polinomok, Salem- és PV-számok) - mátrixgyűrűk (Cayley-Hamilton azonosság tetszőleges gyűrű felett, inverz képzésére zárt részgyűrűk, mátrixok multiplikatív perturbációja, spektrum meghatározása, tridiagonális és ezzel kapcsolatos mátrixok, műszaki alkalmazások) - gyűrűk finom struktúrája (deformációk, végtelen dimenziós Lie-algebrák, infinity algebrák, Morita-ekvivalencia, soros gyűrűk Morita-öndualitása, *-primitív gyűrűk, keresztszorzatok és moduláris csoportalgebrák Lie-tulajdonságai, csoportalgebra egységcsoportja és normalizált egységcsoportja) - radikálelmélet (félig-Abel kategóriák radikáljai és faktorizációs rendszerek, Köthe-probléma, A-radikálok, aktok radikáljai és torzióosztályai) - félcsoportelmélet (félháló-felbontás kategóriai tulajdonságai, félcsoportok kongruenciái) - egyéb (félig-Abel kategóriák és ideálelmélet, endoprimál Abel-csoportok, kompatibilis részbenrendezések kiterjeszthetősége gyűrűkben és általános algebrai struktúrákban, Fitting-lemma, kongruenciaszelidítés, Malcev-feltételek)
Results in English
Results have been obtained in the following topics: - representation theory of algebras (quasi-hereditary algebras, standardly stratified algebras, Coxeter transformation, reciprocal polynomials, Salem and PV numbers) - matrix rings (Cayley-Hamilton identity over an arbitrary ring, subrings closed under taking inverse elements, multiplicative perturbation of matrices, determination of the spectrum, tridiagonal and related matrices, applications in engineering) - structure of rings (deformations, infinite dimensional Lie algebras, infinity algebras, Morita equivalence, Morita selfduality of serial rings, *-primitive rings, Lie properties of crossed products and modular group algebras, unit group and normalized unit group of group algebras) - radical theory (radicals in semi-abelian categories and factorization systems, Koethe problem, A-radicals, radicals and torsion classes of acts) - else (semi-abelian categories and the theory of ideals, endoprimal abelian groups, linear extensibility of compatible partial orders in rings and general algebraic structures, Fitting lemma, tame congruences, Malcev conditions)
Full text http://real.mtak.hu/888/
Decision
Yes





 

List of publications

  
Ánh PN; Siddoway M.: Equivalent endomorphism rings arising from Morita context, Commun Algebra 33: 97-100, 2005
Babcsányi I; Nagy A.: Homomorphic direct product of automata, Publ Math Debrecen Suppl. 65: 513-524, 2004
Balogh Zs; Bovdi A.: Group algebras with unit group of class p, Publ Math Debrecen 65: 261-268, 2004
Beidar KI; Márki L; Mlitz R; Wiegandt R.: Primitive involution rings, Acta Math Hungar 109: 357-368, 2005
Farkas A; Lancaster P; Rózsa P.: Consistency adjustments of pairwise comparison matrices, Numerical Lin Algebra Appl 10: 689-700, 2003
Farkas A; Lancaster P; Rózsa P.: On approximation of positive matrices by transitive matrices, Comput Math Appl 50: 1033-1039, 2005
Farkas A; Rózsa P.: On the non-uniqueness of the solution to the least-squares optimization of pairwise comparison matrices, Acta Polytechn Hungar 1: 4-26, 2004
Bodin D; Fialowski A; Penkava M.: Classification and versal deformations of L(infinity) algebras on a 2|1-dimensional space, Homology Homotopy Appl 7: 55-86, 2005
Fialowski A; Penkava M.: Strongly homotopy Lie algebras of one even and two odd dimesions, J Algebra 283: 125-148, 2005
Fialowski A; Millionschikov D.: Cohomology of some N-graded Lie algebras, Uspekhi Mat. Nauk 59, no.6: 205-206, 2004
Fialowski A; Penkava M.: Versal deformations of 3-dimensional Lie algebras as L(infinity) algebras, Comm Contemp Math 7: 145-165, 2005
Göbel R; Kaarli K; Márki L; Wallutis SL.: Endoprimal torsion-free separable abelian groups, J Algebra Appl 3: 61-73, 2004
Jiang Z; Nagy A.: RGCn commutative (Delta)-semigroups (Corrigendum), Semigroup Forum 67: 468-470, 2003
Kaarli K; Márki L.: Endoprimal abelian groups of torsion-free rank 1, Rend Semin Mat Univ Padova 112: 117-130, 2004
Kaarli K; Márki L.: Endoprimal algebras, Structural Theory of Automata, Semigroups, and Universal Algebra, NATO Science Ser, II Math Phys Chem Vol 207: 169-180, Springer, Dordrecht, 2005
Lakatos P; Losonczi L.: On zeros of reciprocal polynomials of odd degree, J Ineq Pure Appl Math 4 no. 60: 1-18, 2003
Nagy A.: Subdirectly irreducible strongly RGCn-commutative semigroups with a globally idempotent core, Pure Math Appl 13: 383-387, 2002
Nagy A.: Retractable state-finite automata without outputs, Acta Cybern 16: 399-409, 2004
Nagy A.: Commutative monoid congruences of semigroups, Pure Math Appl 13: 389-392, 2002
Lakatos P; Losonczi L.: Self-inversive polynomials whose zeros are on the unit circle, Publ Math Debrecen 65: 409-420, 2004
Nagy A.: Regular RGCn-commutative semigroups, Sci Iran 12: 10-13, 2005
Nagy A.: Permutable semigroups satisfying a non-trivial permutation identity, Acta Sci Math 71: 37-43, 2005
Nagy A.: A supplement to my paper ''Right commutative (Delta)-semigroups'', Acta Sci Math 71: 35-36, 2005
Satyanarayana B; Wiegandt R.: On the f-prime radical of near-rings, In: Near-rings and Near-fields, Hamburg 2003, 293-299, 2005
Tassi G; Rózsa P.: Forces caused by post-tensioning in continuous concrete girders, BMGE Építőmérn Kar Hidak Szerk Tansz Tud Közl 121-130, 2004
Tassi G; Rózsa P.: A mérnök és a matematikus együttműködése tartószerkezeti feladatok megoldásában, In: Nemzetk Építéstud Konf, Csíksomlyó 2004: pp. 377-388, 2004
Tassi G; Rózsa P; Hunyadi M.: Analytical solution of basic equations of theory of structures for cable-stayed bridges, Rakenteiden Mekaniikka 37, no.3: 18-33, 2004
Tumurbat S; Wiegandt R.: Radicals of polynomial rings, Soochow J Math 29: 425-434, 2003
Tumurbat S; Wiegandt R: Radicals around Köthe's problem, Bul Acad Stiinte Repub Mold Mat 1(44): 76-84, 2004
Tumurbat S; Wiegandt R: A-radicals of involution rings, Southeast Asian Math Bull 29: 393-399, 2005
Tumurbat S; Wiegandt R: On A-radicals, Math Slovaca 56: 113-119, 2006
Blass A, Braun G: Random orders and gambler's ruin, Electron J Comb 12, no.1, R.23: 1-27, 2005
Ánh PN; Herbera D.: Müller's question on semiperfect complete hereditary noetherian prime rings, Proc Edinburgh Math Soc 49: 567-573, 2006
Fialowski A; Millionschikov D.: Cohomology of graded Lie algebras of maximal class, J Algebra 296: 157-176, 2006
Fialowski A; de Montigny M.: Deformations and contractions of Lie algebras, J Phys A Math Gen 38: 6335-6349, 2005
Fialowski A; Penkava M.: Examples of miniversal deformations of L(infinity) algebras, Forum Math 19: 463-486, 2007
Foldes S; Szigeti J.: Maximal compatible extensions of partial orders, J Austral Math Soc 81: 245-253, 2006
Körtesi P; Szigeti J.: A general approach to the Fitting Lemma, Mathematika 52: 155-160, 2005
Loi NV; Wiegandt R: On the Amitsur property of radicals, Algebra Discrete Math 3: 92-100, 2006
Loi NV; Wiegandt R: Subdirect irreducibility of algebras and acts with an additional unary operation, Miskolc Math Notes 6: 217-224, 2005
Puczylowski ER; Wiegandt R: Kostia's contribution to radical theory and related topics, In: Rings and Nearrings, Walter de Gruyter, 121-157, 2007
Radeleczki S; Szigeti J: Linear orders on general algebras, Order 22: 41-62, 2005
Szigeti J: Linear orders on rings, Commun Algebra 33: 1-13, 2005
Fried E: Relations among lattice-properties, Acta Sci Math 72: 507-523, 2006
Fried E: Dual discriminator for graph algebras and weak lattices, Acta Sci Math 72: 459-479, 2006
Bovdi A; Grishkov A: Lie properties of crossed products, kozlesre benyujtva, 2008
Bovdi VA; Konovalov AB; Siciliano S: Integral group ring of the Mathieu simple group M12, Rend Circ Mat Palermo (2) 56: 125-136, 2007
Bovdi VA; Srivastava JB: Lie nilpotency indices of modular group algebras, Algebra Colloq, közlésre elfogadva, 2008
Janelidze G; Laan V; Márki L: Limit preservation properties of the greatest semilattice image functor, közlésre leadva, 2008
Janelidze G; Laan V; Márki L: Limit preservation properties of the greatest semilattice image functor on semigroups, Semigroups and Applications, University of Kerala, közlésre elfogadva, 2007
Foldes S; Szigeti J.: A half-space approach to order dimension, "közlésre elfogadva" Order, 2008
Szigeti J; van Wyk L: Subrings which are closed with respect to taking the inverse, ''közlésre elfogadva'' J Algebra, 2008
Fialowski A: Global deformations of Lie algebras, In: Rings, Modules, Algebras, and Abelian Groups, Marcel Dekker, 177-188, 2004
Fialowski A: The moduli space and versal deformations of three dimensional Lie algebras, In: Algebras, Rings and their Representations, World Scientific, 79-91, 2006
Fialowski A; de Montigny M.: On deformations and contractions of Lie algebras, Symmetry, Integrability and In Geometry (SIGMA) Methods Appl 1: 048, 10pp, 2006
Fialowski A; Penkava M.: Deformations of four-dimensional Lie algebras, Comm Contemp Math 9: 41-79, 2007
Fialowski A; Penkava M: Formal deformations, contractions and moduli spaces of Lie algebras, "közlésre elfogadva" Intern J Theor Physics, 2007
Fialowski A: Deformations in mathematics and physics, "közlésre elfogadva" Intern J Theor Physics, 2007
Fialowski A; Schlichenmaier M: Global geometric deformations of the Virasoro algebra, current and affine algebras by Krichever--Novikov type algebra, ''közlésre elfogadva'' Intern J Theor Physics, 2007
Fialowski A; Penkava M: Extensions of L(infinity) algebras of two even and one odd dimension, ''közlésre elfogadva'' Forum Math, 2007
Daily, M; Fialowski A; Penkava M: Comparison of 3-dimensional Z-graded and Z2-graded L(infinity) algebras, ''közlésre elfogadva'' Commun Algebra, 2008
Fialowski A; Wagemann F: Cohomology and deformations of the infinite dimensional Lie algebra m0, ''közlésre elfogadva'' J Algebra, 2008
Nagy A.: Medial permutable semigroups of the first kind, "közlésre leadva", 2008
Nagy A.: Subdirectly irreducible RGC-commutative right H-semigroups, "közlésre leadva", 2008
Babcsányi I; Nagy A.: Semigroups with finite lattices of one-sided congruences, "közlésre leadva", 2008
Lakatos P: Spectral properties of Copxeter transformation, ''közlésre elfogadva'' Southeast Asian Math Bull, 2007
Lakatos P; Losonczi L: Circular interlacing with reciprocal polynomials, ''közlésre elfogadva'' Math Inequal Appl, 2007
Lakatos P: Salem and PV numbers defined by Coxeter, ''közlésre beadva'', 2008
Kearnes, KA; Kiss EW: The triangular principle is equivalent to the triangular scheme, Algebra Universalis 54: 373-383, 2005
Idziak P; Kearnes, KA; Kiss EW; Valeriote M: Definable principal congruences and solvability, "közlésre elfogadva" Annals Pure Appl Logic, 2007
Kearnes, KA; Kiss EW: The Shape of Congruences Lattices, ''közlésre beadva'', 2008
Ágoston I; Dlab V; Lukács E.: Approximation of algebras by standardly stratified algebras, "közlésre benyújtva", 2008
Balogh Zs; Bovdi A.: On units of group algebras of 2-groups of maximal class, Commun Algebra 32: 3227-3245, 2004
Farkas A; György A; Rózsa P.: On the spectrum of pairwise comparison matrices, Linear Algebra Appl 385: 443-462, 2004
Jones PR; Nagy A.: Permutative semigroups whose congruences form a chain, Semigroup Forum 69: 446-456, 2004
Ágoston I; Dlab V; Lukács E.: Standardly stratified extension algebras, Commun Algebra 33: 1357-1368, 2005
Fialowski A; Schlichenmaier M.: Global geometric deformations of current algebras as Krichever-Novikov type algebras, Comm Math Phys 260: 579-612, 2005
Ánh PN: Selfdualities of serial rings, revisited, Bull London Math Soc 38: 411-420, 2006
Szigeti J.: Cayley--Hamilton theorem for matrices over an arbitrary ring, Serdica Math J 32: 269-276, 2006
Wiegandt R: Radical and torsion theory of acts, Semigroup Forum 72: 312-328, 2006
Janelidze G; Márki L; Ursini A: Ideals and clots in universal algebra and in semi-abelian categories, J Algebra 307: 191-208, 2007
Kiss EW; Valeriote M: On tractability and congruence distributivity, Logical Methods Comput Sci 3: 1-20, 2007



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