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Let $S$ be a numerical semigroup. We say that $h \in ℕ ∖ S$ is an isolated gap of $S$ if ${h - 1, h + 1} \subseteq S .$ A numerical semigroup without isolated gaps is called a perfect numerical semigroup. Denote by $m (S)$ the multiplicity of a numerical semigroup $S$ . A covariety is a nonempty family $𝒞$ of numerical semigroups that fulfills the following conditions: there exists the minimum of $𝒞,$ the intersection of two elements of $𝒞$ is again an element of $𝒞$ , and $S ∖ {m (S)} \in 𝒞$ for all $S \in 𝒞$ such that $S \neq min (𝒞) .$ We prove that the set $𝒫 (F) = {S : S$ is a perfect numerical semigroup with...

The effect on associated prime ideals produced by an extension of the base field.

Rodney Y. Sharp (1976)

Mathematica Scandinavica

The equality $I^{2} = Q I$ in Buchsbaum rings

Shiro Goto, Hideto Sakurai (2003)

Rendiconti del Seminario Matematico della Università di Padova

The equations of Rees algebras of ideals with linear presentation.

Bernd Ulrich, Wolmer V. Vasconcelos (1993)

Mathematische Zeitschrift

The Gorenstein Property Depends on Characteristic

HANS-GERT GRÄBE (1984)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

The $h$ -vector of a Gorenstein toric ring of a compressed polytope.

Ohsugi, Hidefumi, Hibi, Takayuki (2005)

The Electronic Journal of Combinatorics [electronic only]

The homological theory of maximal Cohen-Macaulay approximations

Maurice Auslander, Ragnar-Olaf Buchweitz (1989)

Mémoires de la Société Mathématique de France

The index of a vector field tangent to a hypersurface and the signature of the relative jacobian determinant

Xavier Gómez-Mont, Pavao Mardešić (1997)

Annales de l'institut Fourier

Given a real analytic vector field tangent to a hypersurface $V$ with an algebraically isolated singularity we introduce a relative Jacobian determinant in the finite dimensional algebra $\frac{B}{{Ann}_{B} (h)}$ associated with the singularity of the vector field on $V$ . We show that the relative Jacobian generates a 1-dimensional non-zero minimal ideal. With its help we introduce a non-degenerate bilinear pairing, and its signature measures the size of this point with sign. The signature satisfies a law of conservation of...

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Tangent cones at Gorenstein singularities

Tensor products of Clifford modules and linear maximal Cohen-Macaulay modules on quadrics

Tensor products of modules and the rigidity of Tor.

The André-Quillen homology of commutative graded algebras

The Category of Graded Modules.

The Classification of Homogeneous Cohen-Macauly Rings of Finite Representation Type.

The Conductor of one-dimensional Gorenstein Rings in their blowing-up.

The cones associated to some tranversal polymatroids.

The Construction of a Module of Finite Projective Dimension from a Finitely Generated Module of Finite Injective Dimension.

The covariety of perfect numerical semigroups with fixed Frobenius number