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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0002-9947, 01/2019, Volume 371, Issue 2, pp. 949 - 969
We present a new list of irreducible components for the space of k-dimensional holomorphic foliations on P-n, n >= 3, k >= 2... 
MATHEMATICS | irreducible components | Holomorphic foliations | STABILITY
Journal Article
Communications in Algebra, ISSN 0092-7872, 05/2018, Volume 46, Issue 5, pp. 1959 - 1970
We study Auslander-Reiten components of an artin algebra with bounded short cycles, namely, there exists a bound for the depths of maps appearing on short cycles of non-zero non-invertible maps... 
translation quivers | representation-finite algebras | cycles in a module category | Jacobson radical | Auslander-Reiten quiver | tilted algebras | irreducible maps | Auslander-Reiten components | Auslander-Reiten sequences | Auslander–Reiten quiver | Auslander–Reiten sequences | Auslander–Reiten components | QUIVERS | MODULE CATEGORIES | DIRECTING MODULES | MATHEMATICS | Gluing | Algebra | Representations | Combinatorial analysis
Journal Article
Journal of Algebra, ISSN 0021-8693, 10/2016, Volume 464, pp. 198 - 225
For any positive integer d, we determine the irreducible components of the varieties that parametrize the d-dimensional representations of a local truncated path algebra Λ. Here Λ is a quotient KQ... 
Irreducible components | Generic properties of representations | Parametrizing varieties for representations of quivers with relations | MATHEMATICS | ALGEBRAS | QUIVERS | MATRICES | INFINITE ROOT SYSTEMS | INVARIANT-THEORY | MODULE VARIETIES | GRAPHS | Algebra
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 8/2016, Volume 283, Issue 3, pp. 1071 - 1109
.... This fact allows us to develop a natural definition of irreducibility and the corresponding theory of irreducible components for amenable C-semianalytic sets... 
Zariski closure | Irreducibility | 58A07 | 32C25 | C -analytic and C -semianalytic sets | 32C20 | Mathematics | Amenable C -semianalytic sets | Irreducible components | Analytic normalization | Mathematics, general | Secondary 26E05 | Primary 14P15 | C-analytic and C-semianalytic sets | Amenable C-semianalytic sets | MATHEMATICS | NULLSTELLENSATZ
Journal Article
Algebra and Number Theory, ISSN 1937-0652, 2018, Volume 12, Issue 2, pp. 379 - 410
For any truncated path algebra 3 of a quiver, we classify, by way of representation-theoretic invariants, the irreducible components of the parametrizing varieties Rep(d) (Lambda... 
Irreducible components | Generic properties of representations | Varieties of representations | MATHEMATICS | varieties of representations | irreducible components | FINITE-DIMENSIONAL REPRESENTATIONS | INFINITE ROOT SYSTEMS | generic properties of representations | GRAPHS
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 05/2017, Volume 520, pp. 80 - 103
...+1 irreducible components. These components are the closure of the orbits (under strict equivalence) of r... 
Irreducible components | Matrix pencil | Orbits | Kronecker canonical form | Normal rank | Algebraic set | CANONICAL FORM | MATHEMATICS | PERTURBATION-THEORY | MATHEMATICS, APPLIED | GEOMETRIC APPROACH | ORBIT
Journal Article
Izvestiya Mathematics, ISSN 1064-5632, 2016, Volume 80, Issue 1, pp. 263 - 284
We calculate the number of irreducible components of varieties in (C*)(n) determined by generic systems of equations with given Newton polytopes... 
Irreducible components | Newton polytopes | Holomorphic forms | Mixed volume | MATHEMATICS | irreducible components | mixed volume | holomorphic forms | Polytopes | Intersections | Mathematical analysis | Invariants
Journal Article
Communications in Algebra, ISSN 0092-7872, 05/2017, Volume 45, Issue 5, pp. 1953 - 1968
We study the degrees of irreducible morphisms between indecomposable modules lying in generalized standard coherent almost cyclic components of Auslander-Reiten... 
Auslander-Reiten quiver | irreducible morphisms | radical | generalized multicoil | QUIVERS | TUBES | COMPOSITE | MATHEMATICS | INDECOMPOSABLE MODULES | REPRESENTATION-THEORY | ADDITIVE CATEGORIES | SPLIT-SEQUENCES | AUSLANDER-REITEN COMPONENTS | ARTIN-ALGEBRAS | SECTIONAL PATHS | Modules | Algebra | Standards | Coherence
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 2018
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 12/2015, Volume 269, Issue 12, pp. 3689 - 3713
... being negative integers. We consider the restriction of (πν,G) under the subgroup H=SO(n−1,1;K). We prove the appearing of discrete components... 
Complementary series | Representations | Semisimple Lie groups | Irreducible decompositions | MATHEMATICS | RESPECT | SPACES | INTERTWINING-OPERATORS | SUBGROUPS | COMPOSITION SERIES | Geometri | Geometry | Matematisk analys | Mathematical Analysis
Journal Article
Journal of Algebra, ISSN 0021-8693, 2011, Volume 331, Issue 1, pp. 130 - 144
We determine the irreducible components of the variety of d-dimensional modules over the algebra k 〈 α , β 〉 / 〈 α 2 , β 2 , β α + q α β 〉 with q ∈ k... 
Irreducible components | Module varieties | MATHEMATICS | DEGENERATIONS
Journal Article
Communications in Algebra, ISSN 0092-7872, 10/2016, Volume 44, Issue 10, pp. 4165 - 4176
... such investigations.We introduce the notion of P-discrete component of the Auslander-Reiten quiver ΓA as follows. Let { P i} of indA with i ∈ ℕ∞ = ℕ ∪ {∞} be the postprojective... 
Postprojective partitions | Degree | Irreducible morphims | MATHEMATICS | 16E10 | MODULES | 16G70 | PREPROJECTIVE PARTITIONS | IRREDUCIBLE MORPHISMS | ARTIN-ALGEBRAS | 16G20 | Joints | Partitions | Algebra
Journal Article
Studia Mathematica, ISSN 0039-3223, 2014, Volume 220, Issue 3, pp. 221 - 241
We give universal upper bounds on the relative dimensions of isotypic components of a tensor product of representations of the linear group GL(n... 
Harmonic analysis | Dimension of isotypic component | Tensor products of irreducible representations of groups | Beurling-Fourier algebra | MATHEMATICS | tensor products of irreducible representations of groups | harmonic analysis | dimension of isotypic component
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 04/2012, Volume 23, Issue 4, pp. 1250031 - 1250040
...}(S)$ of Nash functions on S is an integral domain. Keeping this notion we develop a satisfactory theory of irreducible components of semialgebraic sets, and we use... 
irreducible semialgebraic set | Nash set | q-Nash set | positivstellensätze | substitution theorem | w-Nash set | irreducible components of a semialgebraic set | Nash function | 17th Hilbert problem and real Nullstellensatz | MATHEMATICS | positivstellensatze | NASH FUNCTIONS | SEPARATION | Manifolds | Theorems | Integrals | Mathematical analysis
Journal Article
Algebras and Representation Theory, ISSN 1386-923X, 4/2015, Volume 18, Issue 2, pp. 323 - 337
We study the non-zero composition of n irreducible morphisms between modules in a regular component of the Auslander-Reiten quiver Γ... 
Associative Rings and Algebras | 16E10 | Non-associative Rings and Algebras | Infinite radical | 16G70 | Commutative Rings and Algebras | Regular components | Mathematics | Irreducible morphisms | 16G20 | MATHEMATICS | Algebra
Journal Article
Izvestiya: Mathematics, ISSN 1064-5632, 08/2011, Volume 75, Issue 4, pp. 711 - 748
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2019, Volume 371, Issue 9, pp. 6289 - 6308
This article deals with the irreducible components of the space of codimension one foliations in a projective space defined by logarithmic forms of a certain degree... 
SPACE | MATHEMATICS | HOLOMORPHIC FOLIATIONS | IRREDUCIBLE COMPONENTS
Journal Article
Journal of Algebra, ISSN 0021-8693, 2010, Volume 323, Issue 4, pp. 1000 - 1011
In this work, we consider standard components of the Auslander–Reiten quiver with trivial valuation... 
Standard components | Covering | Irreducible morphisms | Bypass | Radical | MATHEMATICS | AUSLANDER-REITEN COMPONENTS
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 09/2015, Volume 14, Issue 7, pp. 1550106 - 1-1550106-26
We consider A to be an artin algebra. We study the degrees of irreducible morphisms between modules in Auslander-Reiten components Gamma having only almost... 
Auslander-Reiten quiver | radical | Irreducible morphisms | degrees | MATHEMATICS | MATHEMATICS, APPLIED | QUIVERS | MAPS | COHERENT | COMPOSITE | Integers | Algebra | Representations | Brackets | Mathematical analysis | Modules
Journal Article
Journal of Symbolic Computation, ISSN 0747-7171, 2009, Volume 44, Issue 9, pp. 1114 - 1136
We give a uniform method for the two problems of counting the connected and irreducible components of complex algebraic varieties... 
Irreducible components | Characteristic sets | Differential forms | Connected components | Complexity | MATHEMATICS, APPLIED | ALGORITHM | SYSTEMS | TIME | COMPUTER SCIENCE, THEORY & METHODS | Algorithms
Journal Article
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