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International Journal of Mathematics, ISSN 0129-167X, 06/2012, Volume 23, Issue 6, pp. 1250065 - 1250038
Journal Article
Kodai Mathematical Journal, ISSN 0386-5991, 2015, Volume 38, Issue 1, pp. 201 - 208
In the paper we prove that there exists a simultaneous reduction of one-parameter family of $\mathfrak{m}_{n}$-primary ideals in the ring of germs of... 
Reduction of an ideal | Łojasiewicz exponent | Hilbert-Samuel multiplicity | MATHEMATICS | Lojasiewicz exponent
Journal Article
Journal of Algebra, ISSN 0021-8693, 2008, Volume 319, Issue 5, pp. 1851 - 1869
We show that the only regularity property satisfied by asymptotic invariants of abstract multigraded systems of ideals is convexity, which is imposed formally. 
Asymptotic invariant | Order of vanishing | Graded system of ideals | log-canonical threshold | Hilbert–Samuel multiplicity | Hilbert-Samuel multiplicity | MATHEMATICS | graded system of ideals | order of vanishing | asymptotic invariant
Journal Article
Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 2/2000, Volume 43, Issue 1, pp. 73 - 94
Let (A, m) be a Noetherian local ring such that the residue field A/m is infinite. Let I be arbitrary ideal in A, and hi a finitely generated A-module. We... 
Grothendieck group | Regular local ring | Gorenstein local ring | Hubert-samuel function | Analytic spread | Multiplicity | Hilbert-Samuel function | MATHEMATICS | multiplicity | regular local ring | analytic spread | REES
Journal Article
Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 09/2013, Volume 49, Issue 3, pp. 393 - 412
We study a natural generalization of transversally intersecting smooth hypersurfaces in a complex manifold: hypersurfaces whose components intersect in a... 
Hilbert-Samuel polynomial | Jacobian ideal | Free divisor | Normal crossing divisor | Logarithmic derivations | free divisor | LIE-ALGEBRAS | MATHEMATICS | normal crossing divisor | HYPERSURFACE SINGULARITIES | logarithmic derivations
Journal Article
none We want to discuss the classification of algebraic curves of degree four with a triple point. Then we have the Hilbert-Samuel polynomials and Hilbert... 
algebraic curves | Hilbert series | 代數曲線 | Hilbert-Samuel polynomials | projective
Dissertation
Proceedings of the American Mathematical Society, ISSN 0002-9939, 8/1975, Volume 51, Issue 1, pp. 19 - 24
Let R be a local ring with a maximal ideal m. It is proved that in case R is a Cohen-Macaulay (C.M.) ring and dim m/m - dim R = 1, then the multiplicity of R... 
Mathematical rings | Mathematical functions | Polynomials | Mathematics | Mathematical theorems | Hilbert-Samuel function | Cohen-Macaulay ring
Journal Article
Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 02/2016, Volume 59, Issue 1, pp. 77 - 90
In this paper we consider the problem of explicitly finding canonical ideals of one-dimensional Cohen-Macaulay local rings. We show that Gorenstein ideals... 
Hilbert-Samuel function | Cohen-Macaulay | Gorenstein | canonical ideal | MATHEMATICS | CURVE SINGULARITIES | Geometry | Mathematics | Construction | Singularities | Mathematical analysis | Classification | Rings (mathematics)
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2007, Volume 135, Issue 10, pp. 3073 - 3082
Let R be a local, Noetherian ring and I\subseteq R an ideal. A question of Kodiyalam asks whether for fixed i > 0, the polynomial giving the ith Betti number... 
Functors | Polynomials | Mathematical rings | Mathematical theorems | Applied mathematics | Degrees of polynomials | Hilbert-samuel polynomial | Torsion functor | Quasi-unmixed local ring | LOCAL RINGS | MATHEMATICS | torsion functor | MATHEMATICS, APPLIED | quasi-unmixed local ring | Hilbert-Samuel polynomial
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 03/2007, Volume 135, Issue 3, pp. 637 - 648
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2005, Volume 133, Issue 4, pp. 987 - 993
Let R = \bigoplus _{n \geq 0} R_n be a Noetherian homogeneous ring with one-dimensional local base ring (R_0, {\mathfrak m}_0). Let {\mathfrak q}_0 \subseteq... 
Mathematical constants | Mathematical rings | Polynomials | Algebra | Mathematical theorems | Coefficients | Graded components | Hilbert-Samuel polynomials | Local cohomology modules | MATHEMATICS | MATHEMATICS, APPLIED | RINGS | local cohomology modules | graded components | PRIMES
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 10/1999, Volume 351, Issue 10, pp. 4027 - 4042
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/1996, Volume 124, Issue 5, pp. 1393 - 1401
A d-dimensional version is given of a 2-dimensional result due to C. Huneke. His result produced a formula relating the length \lambda (I^{n+1}/JI^{n}) to the... 
Integers | Algebra | Mathematical induction | Mathematical rings | Polynomials | Mathematical functions | Coefficients | Associated graded ring | Cohen-Macaulay | Hilbert-Samuel polynomial | Depth | MATHEMATICS | MATHEMATICS, APPLIED | depth | associated graded ring | RINGS | IDEALS
Journal Article
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