Sur les algèbres universelles

Micali, Artibano

doi:10.5802/aif.173

Cited by 72 publications

(37 citation statements)

References 3 publications

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“…Symmetric algebras are deeply involved when regularity is concerned. The symmetric algebra SA(M) of an A-module M is absolutely integral over A if and only if M is integrally flat (see [24,Proposition 1]. These observations combine to yield in Proposition 4.4 that an absolutely integral homomorphism with regular fiber rings, between Noetherian rings, preserves regularity.…”

Section: Introduction and Notationmentioning

confidence: 71%

Absolutely integral homomorphisms

Picavet

2007

Journal of Algebra

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Absolutely integral algebras over a field are the subject of a chapter in Field Theory. They are also known as geometrically integral algebras in Algebraic Geometry. We generalize this concept to arbitrary commutative algebras. Our first main result is that a ring homomorphism is absolutely integral if and only if it becomes flat after an integral base change and its fibers are geometrically integral. These homomorphisms are characterized with the help of absolute integral closedness property and do have some transcendence properties. They generally preserve normality, regularity, and the complete intersection property.

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Section: Introduction and Notationmentioning

confidence: 71%

Absolutely integral homomorphisms

Picavet

2007

Journal of Algebra

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“…(See [26,Théorème 1]; see also [6,Proposition 2.4].) An ideal generated by a regular sequence is of linear type.…”

Section: Notations and Linearity Conditionsmentioning

confidence: 99%

A duality approach to the symmetry of Bernstein–Sato polynomials of free divisors

Macarro

2015

Advances in Mathematics

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In this paper we prove that the Bernstein-Sato polynomial of any free divisor for which the D[s]-module D[s]h s admits a Spencer logarithmic resolution satisfies the symmetry property b(−s − 2) = ±b(s). This applies in particular to locally quasi-homogeneous free divisors (for instance, to free hyperplane arrangements), or more generally, to free divisors of linear Jacobian type. We also prove that the Bernstein-Sato polynomial of an integrable logarithmic connection E and of its dual E * with respect to a free divisor of linear Jacobian type are related by the equality b E (s) = ±b E * (−s − 2). Our results are based on the behaviour of the modules D[s]h s and D[s]E[s]h s under duality.

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“…It is well known ( [1] or [3]) that for ideals generated by A -sequences, the symmetric algebra and the Rees algebra are isomorphic. In particular, Qao(ax,.…”

Section: Propositionmentioning

confidence: 99%

Generalized Analytic Independence

Barshay¹

1976

Proceedings of the American Mathematical Society

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Sur les algèbres universelles

Cited by 72 publications

References 3 publications

Absolutely integral homomorphisms

Absolutely integral homomorphisms

A duality approach to the symmetry of Bernstein–Sato polynomials of free divisors

Generalized Analytic Independence

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