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
projekt kezdete
2003-01-01
projekt vége
2007-06-30
aktuális összeg (MFt)
23.767
FTE (kutatóév egyenérték)
0.43
állapot
lezárult projekt
Zárójelentés
kutatási eredmények (magyarul)
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)
kutatási eredmények (angolul)
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)
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
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 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
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
